Phase diagram of generalized XY model using the tensor renormalization group

Samlodia, Abhishek; Longia, Vamika; Jha, Raghav G.; Joseph, Anosh

doi:10.1103/PhysRevD.110.034504

Phase diagram of generalized XY model using the tensor renormalization group

Journal Article · Tue Aug 06 00:00:00 EDT 2024 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.110.034504· OSTI ID:2427028

; ; ;

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless and Ising class. We explore the model for a wide range of temperatures, $T$ , and the deformation parameter, $Δ$ , and compute specific heat along with integer and half-integer magnetic susceptibility, finding both Berezinskii-Kosterlitz-Thouless-like and Ising-like transitions and the region where they meet.

Published by the American Physical Society 2024

View Journal Article

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0019139; AC05-06OR23177; SC0012704

OSTI ID:: 2427028

Alternate ID(s):: OSTI ID: 2428892

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 3 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (30)

Tensor network analysis of critical coupling in two dimensional ϕ4 theory Kadoh, Daisuke; Kuramashi, Yoshinobu; Nakamura, Yoshifumi Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/JHEP05(2019)184	journal	May 2019
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
Transfer matrix in plane-rotator model Mattis, Daniel C. Physics Letters A, Vol. 104, Issue 6-7 https://doi.org/10.1016/0375-9601(84)90816-8	journal	September 1984
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
Ordering, metastability and phase transitions in two-dimensional systems Kosterlitz, J M; Thouless, D J Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203 https://doi.org/10.1088/0022-3719/6/7/010	journal	April 1973
The phase diagram of a generalised XY model Carpenter, D. B.; Chalker, J. T. Journal of Physics: Condensed Matter, Vol. 1, Issue 30 https://doi.org/10.1088/0953-8984/1/30/004	journal	July 1989
Microcanonical Monte Carlo simulations for the two-dimensional XY model Ota, S.; Ota, S. B.; Fahnle, M. Journal of Physics: Condensed Matter, Vol. 4, Issue 24 https://doi.org/10.1088/0953-8984/4/24/011	journal	June 1992
Critical analysis of two-dimensional classical XY model Jha, Raghav G. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2020, Issue 8 https://doi.org/10.1088/1742-5468/aba686	journal	August 2020
Deconfinement transitions in a generalised XY model Serna, Pablo; Chalker, J. T.; Fendley, Paul Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 42 https://doi.org/10.1088/1751-8121/aa89a1	journal	September 2017
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
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
Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks Song, Feng-Feng; Zhang, Guang-Ming Physical Review B, Vol. 103, Issue 2 https://doi.org/10.1103/PhysRevB.103.024518	journal	January 2021
Monte Carlo study of the planar spin model Tobochnik, Jan; Chester, G. V. Physical Review B, Vol. 20, Issue 9 https://doi.org/10.1103/PhysRevB.20.3761	journal	November 1979
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
Variational optimization algorithms for uniform matrix product states Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T. Physical Review B, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevB.97.045145	journal	January 2018
Correlation length in a generalized two-dimensional XY model Nui, Duong Xuan; Tuan, Le; Trung Kien, Nguyen Duc Physical Review B, Vol. 98, Issue 14 https://doi.org/10.1103/PhysRevB.98.144421	journal	October 2018
Phase transition of four-dimensional Ising model with higher-order tensor renormalization group Akiyama, Shinichiro; Kuramashi, Yoshinobu; Yamashita, Takumi Physical Review D, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevD.100.054510	journal	September 2019
Clock model interpolation and symmetry breaking in O(2) models Hostetler, Leon; Zhang, Jin; Sakai, Ryo Physical Review D, Vol. 104, Issue 5 https://doi.org/10.1103/PhysRevD.104.054505	journal	September 2021
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
Moving from continuous to discrete symmetry in the 2D XY model Butt, Nouman; Jin, Xiao-Yong; Osborn, James C. Physical Review D, Vol. 108, Issue 7 https://doi.org/10.1103/PhysRevD.108.074511	journal	October 2023
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 renormalization group study of the non-Abelian Higgs model in two dimensions Bazavov, Alexei; Catterall, Simon; Jha, Raghav G. Physical Review D, Vol. 99, Issue 11 https://doi.org/10.1103/PhysRevD.99.114507	journal	June 2019
Stiffness jump in the generalized X Y model on the square lattice Hübscher, David M.; Wessel, Stefan Physical Review E, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevE.87.062112	journal	June 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
Competing nematic interactions in a generalized X Y model in two and three dimensions Canova, Gabriel A.; Levin, Yan; Arenzon, Jeferson J. Physical Review E, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevE.94.032140	journal	September 2016
New Ordered Phases in a Class of Generalized X Y Models Poderoso, Fábio C.; Arenzon, Jeferson J.; Levin, Yan Physical Review Letters, Vol. 106, Issue 6 https://doi.org/10.1103/PhysRevLett.106.067202	journal	February 2011
Boson Pairing and Unusual Criticality in a Generalized X Y Model Shi, Yifei; Lamacraft, Austen; Fendley, Paul Physical Review Letters, Vol. 107, Issue 24 https://doi.org/10.1103/PhysRevLett.107.240601	journal	December 2011
Strings in two-dimensional classical XY models Lee, D. H.; Grinstein, G. Physical Review Letters, Vol. 55, Issue 5 https://doi.org/10.1103/PhysRevLett.55.541	journal	July 1985
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
Emergent Potts Order in a Coupled Hexatic-Nematic XY model Drouin-Touchette, Victor; Orth, Peter P.; Coleman, Piers Physical Review X, Vol. 12, Issue 1 https://doi.org/10.1103/PhysRevX.12.011043	journal	March 2022

Similar Records

Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization

Journal Article · Sun Jan 21 23:00:00 EST 2024 · Physical Review Letters · OSTI ID:2282227

Deconfined classical criticality in the anisotropic quantum spin-

\frac{1}{2}

XY model on the square lattice

Journal Article · Sun Mar 02 23:00:00 EST 2025 · Physical Review. B · OSTI ID:2526289

Phase diagram of generalized XY model using the tensor renormalization group

Citation Formats

References (30)

Similar Records

Related Subjects