Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system

Bera, Soumya; Nazir, Ahsan; Chin, Alex W.; Baranger, Harold U.; Florens, Serge

doi:10.1103/physrevb.90.075110

Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system

Journal Article · Thu Aug 07 00:00:00 EDT 2014 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/physrevb.90.075110· OSTI ID:1783785

Bera, Soumya ^[1]; Nazir, Ahsan ^[2]; Chin, Alex W. ^[3]; ^[4]; Florens, Serge ^[5]

CNRS and Univ. Grenoble Alpes (France); Duke University, Dept of Physics
Univ. of Manchester (United Kingdom); Imperial College, London (United Kingdom)
Univ. of Cambridge (United Kingdom)
Duke Univ., Durham, NC (United States)
CNRS and Univ. Grenoble Alpes (France)

We develop a systematic variational coherent state expansion for the many-body ground state of the spin-boson model, in which a quantum two-level system is coupled to a continuum of harmonic oscillators. Energetic constraints at the heart of this technique are rationalized in terms of polarons (displacements of the bath states in agreement with classical expectations) and antipolarons (counter- displacements due to quantum tunneling effects). We present a comprehensive study of the ground state two-level system population and coherence as a function of tunneling amplitude, dissipation strength, and bias (akin to asymmetry of the double well potential defining the two-state system). The entanglement among the different environmental modes is investigated by looking at spectroscopic signatures of the bipartite entanglement entropy between a given environmental mode and all the other modes. We observe a drastic change in behavior of this entropy for increasing dissipation, indicative of the entangled nature of the environmental states. In addition, the entropy spreads over a large energy range at strong dissipation, a testimony to the wide entanglement window characterizing the underlying Kondo state. Lastly, comparisons to accurate numerical renormalization group calculations and to the exact Bethe Ansatz solution of the model demonstrate the rapid convergence of our variationally-optimized multi-polaron expansion, suggesting that it should also be a useful tool for dissipative models of greater complexity, as relevant for numerous systems of interest in quantum physics and chemistry.

View Accepted Manuscript (DOE)

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: SC0005237

OSTI ID:: 1783785

Alternate ID(s):: OSTI ID: 1181386

Journal Information:: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 7 Vol. 90; ISSN 1098-0121

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (55)

Diffusion and Localization of a Particle in a Periodic Potential Coupled to a Dissipative Environment Guinea, F.; Hakim, V.; Muramatsu, A. Physical Review Letters, Vol. 54, Issue 4 https://doi.org/10.1103/physrevlett.54.263	journal	January 1985
Global optimization of statistical functions with simulated annealing Goffe, William L.; Ferrier, Gary D.; Rogers, John Journal of Econometrics, Vol. 60, Issue 1-2 https://doi.org/10.1016/0304-4076(94)90038-8	journal	January 1994
Entanglement entropy, decoherence, and quantum phase transitions of a dissipative two-level system Hur, K. Le Annals of Physics, Vol. 323, Issue 9 https://doi.org/10.1016/j.aop.2007.12.003	journal	September 2008
The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment–protein complexes Chin, A. W.; Prior, J.; Rosenbach, R. Nature Physics, Vol. 9, Issue 2 https://doi.org/10.1038/nphys2515	journal	January 2013
Low-Temperature Properties of the Kondo Hamiltonian. Emery, V. J.; Luther, A. MAGNETISM AND MAGNETIC MATERIALS — 1971 Parts 1 and 2, AIP Conference Proceedings https://doi.org/10.1063/1.2953832	conference	January 1972
Consistent treatment of coherent and incoherent energy transfer dynamics using a variational master equation McCutcheon, Dara P. S.; Nazir, Ahsan The Journal of Chemical Physics, Vol. 135, Issue 11 https://doi.org/10.1063/1.3636081	journal	September 2011
Variational calculation of the dynamics of a two level system interacting with a bath Silbey, Robert; Harris, Robert A. The Journal of Chemical Physics, Vol. 80, Issue 6 https://doi.org/10.1063/1.447055	journal	March 1984
Variational calculation of the tunneling system interacting with a heat bath. II. Dynamics of an asymmetric tunneling system Harris, R. A.; Silbey, R. The Journal of Chemical Physics, Vol. 83, Issue 3 https://doi.org/10.1063/1.449469	journal	August 1985
Accuracy of second order perturbation theory in the polaron and variational polaron frames Lee, Chee Kong; Moix, Jeremy; Cao, Jianshu The Journal of Chemical Physics, Vol. 136, Issue 20 https://doi.org/10.1063/1.4722336	journal	May 2012
Numerical path integral techniques for long time dynamics of quantum dissipative systems Makri, Nancy Journal of Mathematical Physics, Vol. 36, Issue 5 https://doi.org/10.1063/1.531046	journal	May 1995
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems Verstraete, F.; Murg, V.; Cirac, J. I. Advances in Physics, Vol. 57, Issue 2 https://doi.org/10.1080/14789940801912366	journal	March 2008
From coherent motion to localization: dynamics of the spin-boson model at zero temperature Wang, Haobin; Thoss, Michael New Journal of Physics, Vol. 10, Issue 11 https://doi.org/10.1088/1367-2630/10/11/115005	journal	November 2008
Chemical Dynamics in Condensed Phases Nitzan, Abraham Oxford University Press https://doi.org/10.1093/oso/9780198529798.001.0001	book	April 2006
Bosonization of a two-level system with dissipation Guinea, F.; Hakim, V.; Muramatsu, A. Physical Review B, Vol. 32, Issue 7 https://doi.org/10.1103/PhysRevB.32.4410	journal	October 1985
Resonant tunneling and low-energy impurity behavior in a resonant-level model Ponomarenko, V. V. Physical Review B, Vol. 48, Issue 8 https://doi.org/10.1103/PhysRevB.48.5265	journal	August 1993
Coherent-incoherent transition in the sub-Ohmic spin-boson model Chin, Alex; Turlakov, Misha Physical Review B, Vol. 73, Issue 7 https://doi.org/10.1103/PhysRevB.73.075311	journal	February 2006
Density matrix renormalization group approach to the spin-boson model Wong, Hang; Chen, Zhi-De Physical Review B, Vol. 77, Issue 17 https://doi.org/10.1103/PhysRevB.77.174305	journal	May 2008
Ultraslow quantum dynamics in a sub-Ohmic heat bath Nalbach, P.; Thorwart, M. Physical Review B, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevB.81.054308	journal	February 2010
Dissipative spin dynamics near a quantum critical point: Numerical renormalization group and Majorana diagrammatics Florens, S.; Freyn, A.; Venturelli, D. Physical Review B, Vol. 84, Issue 15 https://doi.org/10.1103/PhysRevB.84.155110	journal	October 2011
Kondo resonance of a microwave photon Le Hur, Karyn Physical Review B, Vol. 85, Issue 14 https://doi.org/10.1103/PhysRevB.85.140506	journal	April 2012
Ground state and dynamics of the biased dissipative two-state system: Beyond variational polaron theory Nazir, Ahsan; McCutcheon, Dara P. S.; Chin, Alex W. Physical Review B, Vol. 85, Issue 22 https://doi.org/10.1103/PhysRevB.85.224301	journal	June 2012
Nonperturbative stochastic method for driven spin-boson model Orth, Peter P.; Imambekov, Adilet; Le Hur, Karyn Physical Review B, Vol. 87, Issue 1 https://doi.org/10.1103/PhysRevB.87.014305	journal	January 2013
Stabilizing spin coherence through environmental entanglement in strongly dissipative quantum systems Bera, Soumya; Florens, Serge; Baranger, Harold U. Physical Review B, Vol. 89, Issue 12 https://doi.org/10.1103/PhysRevB.89.121108	journal	March 2014
Low- temperature properties of the Kondo Hamiltonian Emery, V. J.; Luther, A. Physical Review B, Vol. 9, Issue 1 https://doi.org/10.1103/PhysRevB.9.215	journal	January 1974
Dynamics of the sub-Ohmic spin-boson model: A comparison of three numerical approaches Yao, Yao; Duan, Liwei; Lü, Zhiguo Physical Review E, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevE.88.023303	journal	August 2013
Sparse Polynomial Space Approach to Dissipative Quantum Systems: Application to the Sub-Ohmic Spin-Boson Model Alvermann, A.; Fehske, H. Physical Review Letters, Vol. 102, Issue 15 https://doi.org/10.1103/PhysRevLett.102.150601	journal	April 2009
Efficient Simulation of Strong System-Environment Interactions Prior, Javier; Chin, Alex W.; Huelga, Susana F. Physical Review Letters, Vol. 105, Issue 5 https://doi.org/10.1103/PhysRevLett.105.050404	journal	July 2010
Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition Chin, Alex W.; Prior, Javier; Huelga, Susana F. Physical Review Letters, Vol. 107, Issue 16 https://doi.org/10.1103/PhysRevLett.107.160601	journal	October 2011
Critical and Strong-Coupling Phases in One- and Two-Bath Spin-Boson Models Guo, Cheng; Weichselbaum, Andreas; von Delft, Jan Physical Review Letters, Vol. 108, Issue 16 https://doi.org/10.1103/PhysRevLett.108.160401	journal	April 2012
Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array Goldstein, Moshe; Devoret, Michel H.; Houzet, Manuel Physical Review Letters, Vol. 110, Issue 1 https://doi.org/10.1103/PhysRevLett.110.017002	journal	January 2013
Multimode Circuit Quantum Electrodynamics with Hybrid Metamaterial Transmission Lines Egger, D. J.; Wilhelm, F. K. Physical Review Letters, Vol. 111, Issue 16 https://doi.org/10.1103/PhysRevLett.111.163601	journal	October 2013
Nonequilibrium and Nonperturbative Dynamics of Ultrastrong Coupling in Open Lines Peropadre, B.; Zueco, D.; Porras, D. Physical Review Letters, Vol. 111, Issue 24 https://doi.org/10.1103/PhysRevLett.111.243602	journal	December 2013
Ground-State Properties in the Kondo Problem Emery, V. J.; Luther, A. Physical Review Letters, Vol. 26, Issue 25 https://doi.org/10.1103/PhysRevLett.26.1547	journal	June 1971
Numerical Renormalization Group for Bosonic Systems and Application to the Sub-Ohmic Spin-Boson Model Bulla, Ralf; Tong, Ning-Hua; Vojta, Matthias Physical Review Letters, Vol. 91, Issue 17 https://doi.org/10.1103/PhysRevLett.91.170601	journal	October 2003
Equilibrium and Nonequilibrium Dynamics of the Sub-Ohmic Spin-Boson Model Anders, Frithjof B.; Bulla, Ralf; Vojta, Matthias Physical Review Letters, Vol. 98, Issue 21 https://doi.org/10.1103/PhysRevLett.98.210402	journal	May 2007
Dynamics of the dissipative two-state system Leggett, A. J.; Chakravarty, S.; Dorsey, A. T. Reviews of Modern Physics, Vol. 59, Issue 1 https://doi.org/10.1103/RevModPhys.59.1	journal	January 1987
Numerical renormalization group method for quantum impurity systems Bulla, Ralf; Costi, Theo A.; Pruschke, Thomas Reviews of Modern Physics, Vol. 80, Issue 2 https://doi.org/10.1103/RevModPhys.80.395	journal	April 2008
A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search Hager, William W.; Zhang, Hongchao SIAM Journal on Optimization, Vol. 16, Issue 1 https://doi.org/10.1137/030601880	journal	January 2005
A Limited Memory Algorithm for Bound Constrained Optimization Byrd, Richard H.; Lu, Peihuang; Nocedal, Jorge SIAM Journal on Scientific Computing, Vol. 16, Issue 5 https://doi.org/10.1137/0916069	journal	September 1995
The Limited Memory Conjugate Gradient Method Hager, William W.; Zhang, Hongchao SIAM Journal on Optimization, Vol. 23, Issue 4 https://doi.org/10.1137/120898097	journal	January 2013
Quantum Dissipative Systems Weiss, Ulrich World Scientific https://doi.org/10.1142/1476	book	January 1993
Quantum Dissipative Systems Weiss, Ulrich https://doi.org/10.1142/4239	book	October 1999
Quantum Dissipative Systems Weiss, Ulrich Series in Modern Condensed Matter Physics, Vol. 13 https://doi.org/10.1142/6738	book	March 2008
Quantum Dissipative Systems Weiss, Ulrich https://doi.org/10.1142/8334	book	March 2012
Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent Hager, William W.; Zhang, Hongchao ACM Transactions on Mathematical Software, Vol. 32, Issue 1 https://doi.org/10.1145/1132973.1132979	journal	March 2006
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization Zhu, Ciyou; Byrd, Richard H.; Lu, Peihuang ACM Transactions on Mathematical Software, Vol. 23, Issue 4 https://doi.org/10.1145/279232.279236	journal	December 1997
Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm Corana, A.; Marchesi, M.; Martini, C. ACM Transactions on Mathematical Software, Vol. 13, Issue 3 https://doi.org/10.1145/29380.29864	journal	September 1987
Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system Hur, Karyn Le arXiv https://doi.org/10.48550/arxiv.0711.2301	text	January 2007
Density matrix renormalization group approach of the spin-boson model Wong, Hang; Chen, Zhi-De arXiv https://doi.org/10.48550/arxiv.0801.3937	text	January 2008
Ultraslow quantum dynamics in a sub-Ohmic heat bath Nalbach, P.; Thorwart, M. arXiv https://doi.org/10.48550/arxiv.0908.2749	text	January 2009
Kondo Resonance of a Microwave Photon Hur, Karyn Le arXiv https://doi.org/10.48550/arxiv.1104.0708	text	January 2011
Dissipative spin dynamics near a quantum critical point: Numerical Renormalization Group and Majorana diagrammatics Florens, Serge; Freyn, Axel; Venturelli, Davide arXiv https://doi.org/10.48550/arxiv.1106.2655	text	January 2011
Nonequilibrium and nonperturbative dynamics of ultrastrong coupling in open lines Peropadre, B.; Zueco, D.; Porras, D. arXiv https://doi.org/10.48550/arxiv.1307.3870	text	January 2013
Stabilizing Spin Coherence Through Environmental Entanglement in Strongly Dissipative Quantum Systems Bera, Soumya; Florens, Serge; Baranger, Harold U. arXiv https://doi.org/10.48550/arxiv.1307.5681	text	January 2013
The numerical renormalization group method for quantum impurity systems Bulla, Ralf; Costi, Theo; Pruschke, Thomas arXiv https://doi.org/10.48550/arxiv.cond-mat/0701105	text	January 2007

Cited By (14)

Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems Iles-Smith, Jake; Lambert, Neill; Nazir, Ahsan Physical Review A, Vol. 90, Issue 3 https://doi.org/10.1103/physreva.90.032114	journal	September 2014
Ground-state phase diagram of the quantum Rabi model Ying, Zu-Jian; Liu, Maoxin; Luo, Hong-Gang Physical Review A, Vol. 92, Issue 5 https://doi.org/10.1103/physreva.92.053823	journal	November 2015
Ultrastrongly dissipative quantum Rabi model Zueco, David; García-Ripoll, Juanjo Physical Review A, Vol. 99, Issue 1 https://doi.org/10.1103/physreva.99.013807	journal	January 2019
Polaron picture of the two-photon quantum Rabi model Cong, Lei; Sun, Xi-Mei; Liu, Maoxin Physical Review A, Vol. 99, Issue 1 https://doi.org/10.1103/physreva.99.013815	journal	January 2019
Quantum phase transitions in the spin-boson model without the counterrotating terms Wang, Yan-Zhi; He, Shu; Duan, Liwei Physical Review B, Vol. 100, Issue 11 https://doi.org/10.1103/physrevb.100.115106	journal	September 2019
Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution Schröder, Florian A. Y. N.; Chin, Alex W. Physical Review B, Vol. 93, Issue 7 https://doi.org/10.1103/physrevb.93.075105	journal	February 2016
Tensor network simulation of polaron-polaritons in organic microcavities del Pino, Javier; Schröder, Florian A. Y. N.; Chin, Alex W. Physical Review B, Vol. 98, Issue 16 https://doi.org/10.1103/physrevb.98.165416	journal	October 2018
Ultrastrong Coupling Few-Photon Scattering Theory Shi, Tao; Chang, Yue; García-Ripoll, Juan José Physical Review Letters, Vol. 120, Issue 15 https://doi.org/10.1103/physrevlett.120.153602	journal	April 2018
Solving Quantum Impurity Problems in and out of Equilibrium with the Variational Approach Ashida, Yuto; Shi, Tao; Bañuls, Mari Carmen Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/physrevlett.121.026805	journal	July 2018
Single Photons by Quenching the Vacuum Sánchez-Burillo, E.; Martín-Moreno, L.; García-Ripoll, J. J. Physical Review Letters, Vol. 123, Issue 1 https://doi.org/10.1103/physrevlett.123.013601	journal	July 2019
Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems Iles-Smith, Jake; Lambert, Neill; Nazir, Ahsan arXiv https://doi.org/10.48550/arxiv.1311.0016	text	January 2013
Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution Schröder, Florian A. Y. N.; Chin, Alex W. arXiv https://doi.org/10.48550/arxiv.1507.02202	text	January 2015
Single photons by quenching the vacuum Sánchez-Burillo, Eduardo; Martín-Moreno, Luis; García-Ripoll, Juan José arXiv https://doi.org/10.48550/arxiv.1810.10857	text	January 2018
Polaron picture of the two-photon quantum Rabi model Cong, Lei; Sun, Xi-Mei; Liu, Maoxin arXiv https://doi.org/10.48550/arxiv.1811.03263	text	January 2018

Similar Records

Conductance of a dissipative quantum dot: Nonequilibrium crossover near a non-Fermi-liquid quantum critical point

Journal Article · Sun Oct 24 20:00:00 EDT 2021 · Physical Review. B · OSTI ID:1854545

Wehrl entropy, Lieb conjecture, and entanglement monotones

Journal Article · Sat Jan 31 23:00:00 EST 2004 · Physical Review. A · OSTI ID:20640709

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
77 NANOSCIENCE AND NANOTECHNOLOGY
open quantum systems
polaron
quantum dissipation
quantum transport
qubit
spin-boson

Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system

Citation Formats

References (55)

Cited By (14)

Similar Records

Related Subjects