Tensor renormalization group for fermions

Akiyama, Shinichiro; Meurice, Yannick; Sakai, Ryo

doi:10.1088/1361-648X/ad4760

Title: Tensor renormalization group for fermions

Journal Article · 28 May 2024 · Journal of Physics. Condensed Matter

DOI: https://doi.org/10.1088/1361-648X/ad4760 · OSTI ID:2367426

;

Abstract We review the basic ideas of the Tensor Renormalization Group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson--Majorana fermions and multi-flavor Gross--Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0010113

OSTI ID:: 2367426

Alternate ID(s):: OSTI ID: 2345844

Journal Information:: Journal of Physics. Condensed Matter, Journal Name: Journal of Physics. Condensed Matter Vol. 36 Journal Issue: 34; ISSN 0953-8984

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (149)

Tensor network renormalization study on the crossover in classical Heisenberg and RP2 models in two dimensions Ueda, Atsushi; Oshikawa, Masaki Physical Review E, Vol. 106, Issue 1 https://doi.org/10.1103/PhysRevE.106.014104	journal	July 2022
Dynamical symmetry breaking in two flavor SU(N) and SO(N) lattice gauge theories Van den Doel, Cees; Smit, Jan Nuclear Physics B, Vol. 228, Issue 1 https://doi.org/10.1016/0550-3213(83)90401-7	journal	November 1983
Tensor network formulation of the massless Schwinger model with staggered fermions Butt, Nouman; Catterall, Simon; Meurice, Yannick Physical Review D, Vol. 101, Issue 9 https://doi.org/10.1103/PhysRevD.101.094509	journal	May 2020
Matrix Product States for Gauge Field Theories Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel Physical Review Letters, Vol. 113, Issue 9 https://doi.org/10.1103/PhysRevLett.113.091601	journal	August 2014
Critical behavior of the lattice Schwinger model with a topological term at θ = π using the Grassmann tensor renormalization group Shimizu, Yuya; Kuramashi, Yoshinobu Physical Review D, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevD.90.074503	journal	October 2014
Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory Kuwahara, Takaaki; Tsuchiya, Asato Progress of Theoretical and Experimental Physics, Vol. 2022, Issue 9 https://doi.org/10.1093/ptep/ptac103	journal	July 2022
Scaling laws for ising models near T c Kadanoff, Leo P. Physics Physique Fizika, Vol. 2, Issue 6 https://doi.org/10.1103/PhysicsPhysiqueFizika.2.263	journal	June 1966
More about the Grassmann tensor renormalization group Akiyama, Shinichiro; Kadoh, Daisuke Journal of High Energy Physics, Vol. 2021, Issue 10 https://doi.org/10.1007/JHEP10(2021)188	journal	October 2021
Real-Time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks Pichler, T.; Dalmonte, M.; Rico, E. Physical Review X, Vol. 6, Issue 1 https://doi.org/10.1103/PhysRevX.6.011023	journal	March 2016
Tensor renormalization group study of the three-dimensional O (2) model Bloch, Jacques; Jha, Raghav G.; Lohmayer, Robert Physical Review D, Vol. 104, Issue 9 https://doi.org/10.1103/PhysRevD.104.094517	journal	November 2021
Grassmann tensor renormalization group for the one-flavor lattice Gross–Neveu model with finite chemical potential Takeda, Shinji; Yoshimura, Yusuke Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 4 https://doi.org/10.1093/ptep/ptv022	journal	April 2015
Formulation of lattice gauge theories for quantum simulations Zohar, Erez; Burrello, Michele Physical Review D, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevD.91.054506	journal	March 2015
Constraints on supersymmetry breaking Witten, Edward Nuclear Physics B, Vol. 202, Issue 2 https://doi.org/10.1016/0550-3213(82)90071-2	journal	July 1982
Tensor network based finite-size scaling for two-dimensional Ising model Huang, Ching-Yu; Chan, Sing-Hong; Kao, Ying-Jer Physical Review B, Vol. 107, Issue 20 https://doi.org/10.1103/PhysRevB.107.205123	journal	May 2023
Simulation of interacting fermions with entanglement renormalization Corboz, Philippe; Evenbly, Glen; Verstraete, Frank Physical Review A, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRevA.81.010303	journal	January 2010
Automatic differentiation for second renormalization of tensor networks Chen, Bin-Bin; Gao, Yuan; Guo, Yi-Bin Physical Review B, Vol. 101, Issue 22 https://doi.org/10.1103/PhysRevB.101.220409	journal	June 2020
Boundary tensor renormalization group Iino, Shumpei; Morita, Satoshi; Kawashima, Naoki Physical Review B, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevB.100.035449	journal	July 2019
Variational Monte Carlo simulation with tensor networks of a pure Z 3 gauge theory in ( 2 + 1 ) D Emonts, Patrick; Bañuls, Mari Carmen; Cirac, Ignacio Physical Review D, Vol. 102, Issue 7 https://doi.org/10.1103/PhysRevD.102.074501	journal	October 2020
Simulating 2 + 1 D Z 3 Lattice Gauge Theory with an Infinite Projected Entangled-Pair State Robaina, Daniel; Bañuls, Mari Carmen; Cirac, J. Ignacio Physical Review Letters, Vol. 126, Issue 5 https://doi.org/10.1103/PhysRevLett.126.050401	journal	February 2021
Tensor renormalization group and the volume independence in 2D U(N) and SU(N) gauge theories Hirasawa, Mitsuaki; Matsumoto, Akira; Nishimura, Jun Journal of High Energy Physics, Vol. 2021, Issue 12 https://doi.org/10.1007/JHEP12(2021)011	journal	December 2021
Entanglement Renormalization Vidal, G. Physical Review Letters, Vol. 99, Issue 22 https://doi.org/10.1103/PhysRevLett.99.220405	journal	November 2007
Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD Bloch, Jacques; Lohmayer, Robert Nuclear Physics B, Vol. 986 https://doi.org/10.1016/j.nuclphysb.2022.116032	journal	January 2023
A practical introduction to tensor networks: Matrix product states and projected entangled pair states Orús, Román Annals of Physics, Vol. 349 https://doi.org/10.1016/j.aop.2014.06.013	journal	October 2014
Fermionic projected entangled pair states Kraus, Christina V.; Schuch, Norbert; Verstraete, Frank Physical Review A, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevA.81.052338	journal	May 2010
New applications of the renormalization group method in physics: a brief introduction Meurice, Y.; Perry, R.; Tsai, S. -W. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 369, Issue 1946 https://doi.org/10.1098/rsta.2011.0117	journal	July 2011
Calculating composite-particle spectra in Hamiltonian formalism and demonstration in 2-flavor QED1+1d Itou, Etsuko; Matsumoto, Akira; Tanizaki, Yuya Journal of High Energy Physics, Vol. 2023, Issue 11 https://doi.org/10.1007/JHEP11(2023)231	journal	November 2023
Competing States in the t - J Model: Uniform d -Wave State versus Stripe State Corboz, Philippe; Rice, T. M.; Troyer, Matthias Physical Review Letters, Vol. 113, Issue 4 https://doi.org/10.1103/PhysRevLett.113.046402	journal	July 2014
Exact lattice supersymmetry Catterall, Simon; Kaplan, David B.; Ünsal, Mithat Physics Reports, Vol. 484, Issue 3-4 https://doi.org/10.1016/j.physrep.2009.09.001	journal	November 2009
Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion Shimizu, Yuya; Kuramashi, Yoshinobu Physical Review D, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevD.97.034502	journal	February 2018
Tensor network approach to two-dimensional Yang–Mills theories Fukuma, Masafumi; Kadoh, Daisuke; Matsumoto, Nobuyuki Progress of Theoretical and Experimental Physics, Vol. 2021, Issue 12 https://doi.org/10.1093/ptep/ptab143	journal	November 2021
Ising model as Wilson-Majorana fermions Wolff, Ulli Nuclear Physics B, Vol. 955 https://doi.org/10.1016/j.nuclphysb.2020.115061	journal	June 2020
Coarse-graining renormalization by higher-order singular value decomposition Xie, Z. Y.; Chen, J.; Qin, M. P. Physical Review B, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevB.86.045139	journal	July 2012
Density matrix formulation for quantum renormalization groups White, Steven R. Physical Review Letters, Vol. 69, Issue 19 https://doi.org/10.1103/PhysRevLett.69.2863	journal	November 1992
Tensor renormalization group approach to ( 1+1 )-dimensional SU(2) principal chiral model at finite density Luo, Xiao; Kuramashi, Yoshinobu Physical Review D, Vol. 107, Issue 9 https://doi.org/10.1103/PhysRevD.107.094509	journal	May 2023
Differentiable Programming Tensor Networks Liao, Hai-Jun; Liu, Jin-Guo; Wang, Lei Physical Review X, Vol. 9, Issue 3 https://doi.org/10.1103/PhysRevX.9.031041	journal	September 2019
Loop Optimization for Tensor Network Renormalization Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang Physical Review Letters, Vol. 118, Issue 11 https://doi.org/10.1103/PhysRevLett.118.110504	journal	March 2017
Bond-weighting method for the Grassmann tensor renormalization group Akiyama, Shinichiro Journal of High Energy Physics, Vol. 2022, Issue 11 https://doi.org/10.1007/JHEP11(2022)030	journal	November 2022
Gauss law, minimal coupling and fermionic PEPS for lattice gauge theories Emonts, Patrick; Zohar, Erez SciPost Physics Lecture Notes https://doi.org/10.21468/SciPostPhysLectNotes.12	journal	January 2020
Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model with tensor-network-based level spectroscopy Ueda, Atsushi; Oshikawa, Masaki Physical Review B, Vol. 104, Issue 16 https://doi.org/10.1103/PhysRevB.104.165132	journal	October 2021
Notes on Migdal's recursion formulas Kadanoff, Leo P. Annals of Physics, Vol. 100, Issue 1-2 https://doi.org/10.1016/0003-4916(76)90066-X	journal	September 1976
Restoration of chiral symmetry in cold and dense Nambu-Jona-Lasinio model with tensor renormalization group Akiyama, Shinichiro; Kuramashi, Yoshinobu; Yamashita, Takumi Journal of High Energy Physics, Vol. 2021, Issue 1 https://doi.org/10.1007/JHEP01(2021)121	journal	January 2021
Renormalization of tensor-network states Zhao, H. H.; Xie, Z. Y.; Chen, Q. N. Physical Review B, Vol. 81, Issue 17 https://doi.org/10.1103/PhysRevB.81.174411	journal	May 2010
Infinite time-evolving block decimation algorithm beyond unitary evolution Orús, R.; Vidal, G. Physical Review B, Vol. 78, Issue 15 https://doi.org/10.1103/PhysRevB.78.155117	journal	October 2008
Finite-size and finite bond dimension effects of tensor network renormalization Ueda, Atsushi; Oshikawa, Masaki Physical Review B, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRevB.108.024413	journal	July 2023
Diagonalizing Transfer Matrices and Matrix Product Operators: A Medley of Exact and Computational Methods Haegeman, Jutho; Verstraete, Frank Annual Review of Condensed Matter Physics, Vol. 8, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031016-025507	journal	March 2017
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations Troyer, Matthias; Wiese, Uwe-Jens Physical Review Letters, Vol. 94, Issue 17 https://doi.org/10.1103/PhysRevLett.94.170201	journal	May 2005
Exact blocking formulas for spin and gauge models Liu, Yuzhi; Meurice, Y.; Qin, M. P. Physical Review D, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevD.88.056005	journal	September 2013
Tensor Networks for Lattice Gauge Theories and Atomic Quantum Simulation Rico, E.; Pichler, T.; Dalmonte, M. Physical Review Letters, Vol. 112, Issue 20 https://doi.org/10.1103/PhysRevLett.112.201601	journal	May 2014
The density-matrix renormalization group Schollwöck, U. Reviews of Modern Physics, Vol. 77, Issue 1 https://doi.org/10.1103/RevModPhys.77.259	journal	April 2005
Tensor renormalization group study of (3+1)-dimensional ℤ2 gauge-Higgs model at finite density Akiyama, Shinichiro; Kuramashi, Yoshinobu Journal of High Energy Physics, Vol. 2022, Issue 5 https://doi.org/10.1007/JHEP05(2022)102	journal	May 2022
Progress towards quantum simulating the classical O ( 2 ) model Zou, Haiyuan; Liu, Yuzhi; Lai, Chen-Yen Physical Review A, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevA.90.063603	journal	December 2014
Tensor renormalization group with randomized singular value decomposition Morita, Satoshi; Igarashi, Ryo; Zhao, Hui-Hai Physical Review E, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevE.97.033310	journal	March 2018
Correlated electrons in high-temperature superconductors Dagotto, Elbio Reviews of Modern Physics, Vol. 66, Issue 3 https://doi.org/10.1103/RevModPhys.66.763	journal	July 1994
Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model Shimizu, Yuya; Kuramashi, Yoshinobu Physical Review D, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevD.90.014508	journal	July 2014
Tensor lattice field theory for renormalization and quantum computing Meurice, Yannick; Sakai, Ryo; Unmuth-Yockey, Judah Reviews of Modern Physics, Vol. 94, Issue 2 https://doi.org/10.1103/RevModPhys.94.025005	journal	May 2022
Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a θ term Kuramashi, Yoshinobu; Yoshimura, Yusuke Journal of High Energy Physics, Vol. 2020, Issue 4 https://doi.org/10.1007/JHEP04(2020)089	journal	April 2020
Full QCD and QED at finite temperature and chemical potential Bender, I.; Hashimoto, T.; Karsch, F. Nuclear Physics B - Proceedings Supplements, Vol. 26 https://doi.org/10.1016/0920-5632(92)90265-T	journal	January 1992
Examples of symmetry-preserving truncations in tensor field theory Meurice, Yannick Physical Review D, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevD.100.014506	journal	July 2019
O(3) nonlinear sigma model in 1 + 1 dimensions with matrix product states Bruckmann, Falk; Jansen, Karl; Kühn, Stefan Physical Review D, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevD.99.074501	journal	April 2019
Metal–insulator transition in the (2+1)-dimensional Hubbard model with the tensor renormalization group Akiyama, Shinichiro; Kuramashi, Yoshinobu; Yamashita, Takumi Progress of Theoretical and Experimental Physics, Vol. 2022, Issue 2 https://doi.org/10.1093/ptep/ptac014	journal	January 2022
Tensor renormalization group approach to ( 1+1 )-dimensional Hubbard model Akiyama, Shinichiro; Kuramashi, Yoshinobu Physical Review D, Vol. 104, Issue 1 https://doi.org/10.1103/PhysRevD.104.014504	journal	July 2021
Phase structure of the CP(1) model in the presence of a topological θ -term Nakayama, Katsumasa; Funcke, Lena; Jansen, Karl Physical Review D, Vol. 105, Issue 5 https://doi.org/10.1103/PhysRevD.105.054507	journal	March 2022
The Hubbard Model: A Computational Perspective Qin, Mingpu; Schäfer, Thomas; Andergassen, Sabine Annual Review of Condensed Matter Physics, Vol. 13, Issue 1 https://doi.org/10.1146/annurev-conmatphys-090921-033948	journal	November 2021
Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model Dempsey, Ross; Klebanov, Igor R.; Pufu, Silviu S. Physical Review Research, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevResearch.4.043133	journal	November 2022
Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains Dukelsky, J.; Martín-Delgado, M. A.; Nishino, T. Europhysics Letters (EPL), Vol. 43, Issue 4 https://doi.org/10.1209/epl/i1998-00381-x	journal	August 1998
Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model Meurice, Y. Journal of Physics A: Mathematical and Theoretical, Vol. 40, Issue 23 https://doi.org/10.1088/1751-8113/40/23/R01	journal	May 2007
Revisiting the local potential approximation of the exact renormalization group equation Bervillier, C. Nuclear Physics B, Vol. 876, Issue 2 https://doi.org/10.1016/j.nuclphysb.2013.08.008	journal	November 2013
Renormalization of tensor networks using graph-independent local truncations Hauru, Markus; Delcamp, Clement; Mizera, Sebastian Physical Review B, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevB.97.045111	journal	January 2018
Image-processing the topological charge density in the $\mathbb{C}P^{N-1}$ model Abe, Yuya; Fukushima, Kenji; Hidaka, Yoshimasa Progress of Theoretical and Experimental Physics, Vol. 2020, Issue 1 https://doi.org/10.1093/ptep/ptz134	journal	January 2020
Tensor network simulation of QED on infinite lattices: Learning from (1+1) d , and prospects for (2+1) d Zapp, Kai; Orús, Román Physical Review D, Vol. 95, Issue 11 https://doi.org/10.1103/PhysRevD.95.114508	journal	June 2017
Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension Lieb, Elliott H.; Wu, F. Y. Physical Review Letters, Vol. 20, Issue 25 https://doi.org/10.1103/PhysRevLett.20.1445	journal	June 1968
Strong coupling QCD at finite baryon-number density Karsch, F.; Mütter, K. -H. Nuclear Physics B, Vol. 313, Issue 3 https://doi.org/10.1016/0550-3213(89)90396-9	journal	February 1989
Tensor Renormalization Group Approach to Two-Dimensional Classical Lattice Models Levin, Michael; Nave, Cody P. Physical Review Letters, Vol. 99, Issue 12 https://doi.org/10.1103/PhysRevLett.99.120601	journal	September 2007
Bold Diagrammatic Monte Carlo Technique: When the Sign Problem Is Welcome Prokof’ev, Nikolay; Svistunov, Boris Physical Review Letters, Vol. 99, Issue 25 https://doi.org/10.1103/PhysRevLett.99.250201	journal	December 2007
Efficient Classical Simulation of Slightly Entangled Quantum Computations Vidal, Guifré Physical Review Letters, Vol. 91, Issue 14 https://doi.org/10.1103/PhysRevLett.91.147902	journal	October 2003
Confinement and String Breaking for QED 2 in the Hamiltonian Picture Buyens, Boye; Haegeman, Jutho; Verschelde, Henri Physical Review X, Vol. 6, Issue 4 https://doi.org/10.1103/PhysRevX.6.041040	journal	November 2016
Non-perturbative renormalization flow in quantum field theory and statistical physics Berges, Jürgen; Tetradis, Nikolaos; Wetterich, Christof Physics Reports, Vol. 363, Issue 4-6 https://doi.org/10.1016/S0370-1573(01)00098-9	journal	June 2002
Corner Transfer Matrix Renormalization Group Method Nishino, Tomotoshi; Okunishi, Kouichi Journal of the Physical Society of Japan, Vol. 65, Issue 4 https://doi.org/10.1143/JPSJ.65.891	journal	April 1996
Accurate exponents from approximate tensor renormalizations Meurice, Y. Physical Review B, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevB.87.064422	journal	February 2013
NJL-model analysis of dense quark matter Buballa, M. Physics Reports, Vol. 407, Issue 4-6 https://doi.org/10.1016/j.physrep.2004.11.004	journal	February 2005
The mass spectrum of the Schwinger model with matrix product states Bañuls, M. C.; Cichy, K.; Cirac, J. I. Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)158	journal	November 2013
Bond-weighted tensor renormalization group Adachi, Daiki; Okubo, Tsuyoshi; Todo, Synge Physical Review B, Vol. 105, Issue 6 https://doi.org/10.1103/PhysRevB.105.L060402	journal	February 2022
Simulation strategies for the massless lattice Schwinger model in the dual formulation Göschl, Daniel; Gattringer, Christof; Lehmann, Alexander Nuclear Physics B, Vol. 924 https://doi.org/10.1016/j.nuclphysb.2017.09.006	journal	November 2017
Existence of a phase-transition in a one-dimensional Ising ferromagnet Dyson, Freeman J. Communications in Mathematical Physics, Vol. 12, Issue 2 https://doi.org/10.1007/BF01645907	journal	June 1969
A Multilinear Singular Value Decomposition De Lathauwer, Lieven; De Moor, Bart; Vandewalle, Joos SIAM Journal on Matrix Analysis and Applications, Vol. 21, Issue 4 https://doi.org/10.1137/S0895479896305696	journal	January 2000
Renormalization and tensor product states in spin chains and lattices Cirac, J. Ignacio; Verstraete, Frank Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 50 https://doi.org/10.1088/1751-8113/42/50/504004	journal	December 2009
The renormalization group: Critical phenomena and the Kondo problem Wilson, Kenneth G. Reviews of Modern Physics, Vol. 47, Issue 4 https://doi.org/10.1103/RevModPhys.47.773	journal	October 1975
Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1) -dimensional compact QED with dynamical fermions at finite density Bender, Julian; Emonts, Patrick; Cirac, J. Ignacio Physical Review Research, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevResearch.5.043128	journal	November 2023
Ising Model with a Scaling Interaction Baker, George A. Physical Review B, Vol. 5, Issue 7 https://doi.org/10.1103/PhysRevB.5.2622	journal	April 1972
Controlling sign problems in spin models using tensor renormalization Denbleyker, Alan; Liu, Yuzhi; Meurice, Y. Physical Review D, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevD.89.016008	journal	January 2014
Fermionic Gaussian projected entangled pair states in 3+1D : Rotations and relativistic limits Emonts, Patrick; Zohar, Erez Physical Review D, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevD.108.014514	journal	July 2023
The Hubbard model - an introduction and selected rigorous results Tasaki, Hal Journal of Physics: Condensed Matter, Vol. 10, Issue 20 https://doi.org/10.1088/0953-8984/10/20/004	journal	May 1998
Correlated fermions on a lattice in high dimensions M�ller-Hartmann, E. Zeitschrift f�r Physik B Condensed Matter, Vol. 74, Issue 4 https://doi.org/10.1007/BF01311397	journal	December 1989
Efficient simulation of Grassmann tensor product states Gu, Zheng-Cheng Physical Review B, Vol. 88, Issue 11 https://doi.org/10.1103/PhysRevB.88.115139	journal	September 2013
Tensor renormalization group study of classical X Y model on the square lattice Yu, J. F.; Xie, Z. Y.; Meurice, Y. Physical Review E, Vol. 89, Issue 1 https://doi.org/10.1103/PhysRevE.89.013308	journal	January 2014
Tensor Network Renormalization Evenbly, G.; Vidal, G. Physical Review Letters, Vol. 115, Issue 18 https://doi.org/10.1103/PhysRevLett.115.180405	journal	October 2015
Two-Dimensional Quantum-Link Lattice Quantum Electrodynamics at Finite Density Felser, Timo; Silvi, Pietro; Collura, Mario Physical Review X, Vol. 10, Issue 4 https://doi.org/10.1103/PhysRevX.10.041040	journal	November 2020
Higher-order tensor renormalization group for relativistic fermion systems Sakai, Ryo; Takeda, Shinji; Yoshimura, Yusuke Progress of Theoretical and Experimental Physics, Vol. 2017, Issue 6 https://doi.org/10.1093/ptep/ptx080	journal	June 2017
Two-Dimensional Tensor Product Variational Formulation Nishino, T.; Hieida, Y.; Okunishi, K. Progress of Theoretical Physics, Vol. 105, Issue 3 https://doi.org/10.1143/PTP.105.409	journal	March 2001
Tensor network formulation for two-dimensional lattice N $$ \mathcal{N} $$ = 1 Wess-Zumino model Kadoh, Daisuke; Kuramashi, Yoshinobu; Nakamura, Yoshifumi Journal of High Energy Physics, Vol. 2018, Issue 3 https://doi.org/10.1007/JHEP03(2018)141	journal	March 2018
Review on novel methods for lattice gauge theories Carmen Bañuls, Mari; Cichy, Krzysztof Reports on Progress in Physics, Vol. 83, Issue 2 https://doi.org/10.1088/1361-6633/ab6311	journal	January 2020
On the Best Rank-1 and Rank-( R ₁ , R ₂ ,. . ., R _N ) Approximation of Higher-Order Tensors De Lathauwer, Lieven; De Moor, Bart; Vandewalle, Joos SIAM Journal on Matrix Analysis and Applications, Vol. 21, Issue 4 https://doi.org/10.1137/S0895479898346995	journal	January 2000
Efficient Basis Formulation for ( 1 + 1 )-Dimensional SU(2) Lattice Gauge Theory: Spectral Calculations with Matrix Product States Bañuls, Mari Carmen; Cichy, Krzysztof; Cirac, J. Ignacio Physical Review X, Vol. 7, Issue 4 https://doi.org/10.1103/PhysRevX.7.041046	journal	November 2017
Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks Magnifico, Giuseppe; Felser, Timo; Silvi, Pietro Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-23646-3	journal	June 2021
Tensor Networks for Lattice Gauge Theories with Continuous Groups Tagliacozzo, L.; Celi, A.; Lewenstein, M. Physical Review X, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevX.4.041024	journal	November 2014
Real-space renormalization in statistical mechanics Efrati, Efi; Wang, Zhe; Kolan, Amy Reviews of Modern Physics, Vol. 86, Issue 2 https://doi.org/10.1103/RevModPhys.86.647	journal	May 2014
Thermodynamic Limit of Density Matrix Renormalization Östlund, Stellan; Rommer, Stefan Physical Review Letters, Vol. 75, Issue 19 https://doi.org/10.1103/PhysRevLett.75.3537	journal	November 1995
GPU-acceleration of tensor renormalization with PyTorch using CUDA Jha, Raghav G.; Samlodia, Abhishek Computer Physics Communications, Vol. 294 https://doi.org/10.1016/j.cpc.2023.108941	journal	January 2024
Finding the ground state of a lattice gauge theory with fermionic tensor networks: A 2+1D Z2 demonstration Emonts, Patrick; Kelman, Ariel; Borla, Umberto Physical Review D, Vol. 107, Issue 1 https://doi.org/10.1103/PhysRevD.107.014505	journal	January 2023
Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density Akiyama, Shinichiro Physical Review D, Vol. 108, Issue 3 https://doi.org/10.1103/PhysRevD.108.034514	journal	August 2023
The density-matrix renormalization group: a short introduction Schollwöck, Ulrich Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 369, Issue 1946 https://doi.org/10.1098/rsta.2010.0382	journal	July 2011
Anisotropic tensor renormalization group Adachi, Daiki; Okubo, Tsuyoshi; Todo, Synge Physical Review B, Vol. 102, Issue 5 https://doi.org/10.1103/PhysRevB.102.054432	journal	August 2020
High-accuracy scaling exponents in the local potential approximation Bervillier, Claude; Jüttner, Andreas; Litim, Daniel F. Nuclear Physics B, Vol. 783, Issue 3 https://doi.org/10.1016/j.nuclphysb.2007.03.036	journal	November 2007
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems Cirac, J. Ignacio; Pérez-García, David; Schuch, Norbert Reviews of Modern Physics, Vol. 93, Issue 4 https://doi.org/10.1103/RevModPhys.93.045003	journal	December 2021
Building projected entangled pair states with a local gauge symmetry Zohar, Erez; Burrello, Michele New Journal of Physics, Vol. 18, Issue 4 https://doi.org/10.1088/1367-2630/18/4/043008	journal	April 2016
Second Renormalization of Tensor-Network States Xie, Z. Y.; Jiang, H. C.; Chen, Q. N. Physical Review Letters, Vol. 103, Issue 16 https://doi.org/10.1103/PhysRevLett.103.160601	journal	October 2009
Fermion bag approach to lattice field theories Chandrasekharan, Shailesh Physical Review D, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevD.82.025007	journal	July 2010
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevX.5.041041	journal	December 2015
All-mode renormalization for tensor network with stochastic noise Arai, Erika; Ohki, Hiroshi; Takeda, Shinji Physical Review D, Vol. 107, Issue 11 https://doi.org/10.1103/PhysRevD.107.114515	journal	June 2023
The density-matrix renormalization group in the age of matrix product states Schollwöck, Ulrich Annals of Physics, Vol. 326, Issue 1 https://doi.org/10.1016/j.aop.2010.09.012	journal	January 2011
A new technique to incorporate multiple fermion flavors in tensor renormalization group method for lattice gauge theories Yosprakob, Atis; Nishimura, Jun; Okunishi, Kouichi Journal of High Energy Physics, Vol. 2023, Issue 11 https://doi.org/10.1007/JHEP11(2023)187	journal	November 2023
Solving the sign problems of the massless lattice Schwinger model with a dual formulation Gattringer, Christof; Kloiber, Thomas; Sazonov, Vasily Nuclear Physics B, Vol. 897 https://doi.org/10.1016/j.nuclphysb.2015.06.017	journal	August 2015
Combining tensor networks with Monte Carlo methods for lattice gauge theories Zohar, Erez; Cirac, J. Ignacio Physical Review D, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevD.97.034510	journal	February 2018
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order Gu, Zheng-Cheng; Wen, Xiao-Gang Physical Review B, Vol. 80, Issue 15 https://doi.org/10.1103/PhysRevB.80.155131	journal	October 2009
Non-Abelian string breaking phenomena with matrix product states Kühn, Stefan; Zohar, Erez; Cirac, J. Ignacio Journal of High Energy Physics, Vol. 2015, Issue 7 https://doi.org/10.1007/JHEP07(2015)130	journal	July 2015
Developments in the Tensor Network — from Statistical Mechanics to Quantum Entanglement Okunishi, Kouichi; Nishino, Tomotoshi; Ueda, Hiroshi Journal of the Physical Society of Japan, Vol. 91, Issue 6 https://doi.org/10.7566/JPSJ.91.062001	journal	June 2022
Strong coupling lattice Schwinger model on large spherelike lattices Gausterer, H.; Lang, C. B. Nuclear Physics B, Vol. 455, Issue 3 https://doi.org/10.1016/0550-3213(95)00533-X	journal	September 1995
DMRG study of the higher-charge Schwinger model and its ’t Hooft anomaly Honda, Masazumi; Itou, Etsuko; Tanizaki, Yuya Journal of High Energy Physics, Vol. 2022, Issue 11 https://doi.org/10.1007/JHEP11(2022)141	journal	November 2022
Lattice QCD with fermions at strong coupling: A dimer system Rossi, Pietro; Wolff, Ulli Nuclear Physics B, Vol. 248, Issue 1 https://doi.org/10.1016/0550-3213(84)90589-3	journal	December 1984
Improved local truncation schemes for the higher-order tensor renormalization group method Bloch, Jacques; Lohmayer, Robert; Meister, Maximilian Nuclear Physics B, Vol. 987 https://doi.org/10.1016/j.nuclphysb.2023.116107	journal	February 2023
Density matrix renormalization group approach to the massive Schwinger model Byrnes, T. M. R.; Sriganesh, P.; Bursill, R. J. Physical Review D, Vol. 66, Issue 1 https://doi.org/10.1103/PhysRevD.66.013002	journal	July 2002
Schwinger model on an interval: Analytic results and DMRG Okuda, Takuya Physical Review D, Vol. 107, Issue 5 https://doi.org/10.1103/PhysRevD.107.054506	journal	March 2023
Efficient Tensor Network Ansatz for High-Dimensional Quantum Many-Body Problems Felser, Timo; Notarnicola, Simone; Montangero, Simone Physical Review Letters, Vol. 126, Issue 17 https://doi.org/10.1103/PhysRevLett.126.170603	journal	April 2021
Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group Yoshimura, Yusuke; Kuramashi, Yoshinobu; Nakamura, Yoshifumi Physical Review D, Vol. 97, Issue 5 https://doi.org/10.1103/PhysRevD.97.054511	journal	March 2018
Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories Meurice, Yannick Physical Review D, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevD.102.014506	journal	July 2020
The Hubbard Model Arovas, Daniel P.; Berg, Erez; Kivelson, Steven A. Annual Review of Condensed Matter Physics, Vol. 13, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031620-102024	journal	November 2021
Correlated Lattice Fermions in d = ∞ Dimensions Metzner, Walter; Vollhardt, Dieter Physical Review Letters, Vol. 62, Issue 3 https://doi.org/10.1103/PhysRevLett.62.324	journal	January 1989
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions Georges, Antoine; Kotliar, Gabriel; Krauth, Werner Reviews of Modern Physics, Vol. 68, Issue 1 https://doi.org/10.1103/RevModPhys.68.13	journal	January 1996
Decorated tensor network renormalization for lattice gauge theories and spin foam models Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian New Journal of Physics, Vol. 18, Issue 5 https://doi.org/10.1088/1367-2630/18/5/053009	journal	May 2016
Improved coarse-graining methods for two dimensional tensor networks including fermions Asaduzzaman, Muhammad; Catterall, Simon; Meurice, Yannick Journal of High Energy Physics, Vol. 2023, Issue 1 https://doi.org/10.1007/JHEP01(2023)024	journal	January 2023
Contraction of fermionic operator circuits and the simulation of strongly correlated fermions Barthel, Thomas; Pineda, Carlos; Eisert, Jens Physical Review A, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevA.80.042333	journal	October 2009
Scaling Hypothesis for Matrix Product States Vanhecke, Bram; Haegeman, Jutho; Van Acoleyen, Karel Physical Review Letters, Vol. 123, Issue 25 https://doi.org/10.1103/PhysRevLett.123.250604	journal	December 2019
Finite-density phase diagram of a ( 1 + 1 ) − d non-abelian lattice gauge theory with tensor networks Silvi, Pietro; Rico, Enrique; Dalmonte, Marcello Quantum, Vol. 1 https://doi.org/10.22331/q-2017-04-25-9	journal	April 2017
Scaling dimensions from linearized tensor renormalization group transformations Lyu, Xinliang; Xu, RuQing G.; Kawashima, Naoki Physical Review Research, Vol. 3, Issue 2 https://doi.org/10.1103/PhysRevResearch.3.023048	journal	April 2021
Fermion sign problem in path integral Monte Carlo simulations: grand-canonical ensemble Dornheim, Tobias Journal of Physics A: Mathematical and Theoretical, Vol. 54, Issue 33 https://doi.org/10.1088/1751-8121/ac1481	journal	July 2021
Algorithms for tensor network renormalization Evenbly, G. Physical Review B, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevB.95.045117	journal	January 2017
Phase structure of NJL model with weak renormalization group Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi Nuclear Physics B, Vol. 931 https://doi.org/10.1016/j.nuclphysb.2018.04.005	journal	June 2018
The renormalization group and the ε expansion Wilson, K. Physics Reports, Vol. 12, Issue 2 https://doi.org/10.1016/0370-1573(74)90023-4	journal	August 1974
Stable Optimization of a Tensor Product Variational State Gendiar, A.; Maeshima, N.; Nishino, T. Progress of Theoretical Physics, Vol. 110, Issue 4 https://doi.org/10.1143/PTP.110.691	journal	October 2003

Similar Records

Improved coarse-graining methods for two dimensional tensor networks including fermions

Journal Article · 2023 · Journal of High Energy Physics (Online) · OSTI ID:2242474

Asaduzzaman, Muhammad; Catterall, Simon; Meurice, Yannick; +2 more

Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm

Journal Article · 2021 · Physical Review. D. · OSTI ID:1772672

Liu, Hanqing; Chandrasekharan, Shailesh; Kaul, Ribhu K.

Perturbative renormalization factors and O(a{sup 2}) corrections for lattice four-fermion operators with improved fermion/gluon actions

Journal Article · 2011 · Physical Review. D, Particles Fields · OSTI ID:21537729

Constantinou, Martha; Panagopoulos, Haralambos; Skouroupathis, Apostolos; +4 more

Title: Tensor renormalization group for fermions

Citation Formats

References (149)

Similar Records

Related Subjects