Pairwise connected tensor network representation of path integrals

被引:17
作者
Bose, Amartya [1 ]
机构
[1] Princeton Univ, Dept Chem, Princeton, NJ 08544 USA
关键词
MATRIX RENORMALIZATION-GROUP; REDUCED DENSITY-MATRICES; QUANTUM TIME EVOLUTION; RATE CONSTANTS; PROPAGATOR; DYNAMICS; MEMORY; FORMULATION; BATH;
D O I
10.1103/PhysRevB.105.024309
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
It has been recently shown how the tensorial nature of real-time path integrals (PIs) involving the Feynman-Vernon influence functional can be utilized with matrix product states, taking advantage of the finite length of the bath-induced memory. Tensor networks (TNs) promise to provide a unified language to express the structure of a PI. Here, a generalized TN specifically incorporating the pairwise interaction structure of the influence functional and its invariance with respect to the average forward-backward position or the sojourn value in the form of the blip representation is derived and implemented. This pairwise connected TNPI (PC-TNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage and performance scalings are reported, showing the compactness of the representation and the efficiency of the contraction process. Finally, taking advantage of the compressed representation, the viability of using PC-TNPI for simulating multistate problems is demonstrated. The PC-TNPI structure can be shown to yield other TN algorithms currently in use. Consequently, it should be possible to use it as a starting point for deriving other optimized procedures.
引用
收藏
页数:11
相关论文
共 52 条
[41]   Efficient non-Markovian quantum dynamics using time-evolving matrix product operators [J].
Strathearn, A. ;
Kirton, P. ;
Kilda, D. ;
Keeling, J. ;
Lovett, B. W. .
NATURE COMMUNICATIONS, 2018, 9
[42]  
Strathearn A., 2020, Modelling non-Markovian quantum systems using tensor networks
[43]   QUASI-ADIABATIC PROPAGATOR PATH-INTEGRAL METHODS - EXACT QUANTUM RATE CONSTANTS FOR CONDENSED-PHASE REACTIONS [J].
TOPALER, M ;
MAKRI, N .
CHEMICAL PHYSICS LETTERS, 1993, 210 (1-3) :285-293
[44]   QUANTUM RATES FOR A DOUBLE-WELL COUPLED TO A DISSIPATIVE BATH - ACCURATE PATH-INTEGRAL RESULTS AND COMPARISON WITH APPROXIMATE THEORIES [J].
TOPALER, M ;
MAKRI, N .
JOURNAL OF CHEMICAL PHYSICS, 1994, 101 (09) :7500-7519
[45]   Entanglement renormalization [J].
Vidal, G. .
PHYSICAL REVIEW LETTERS, 2007, 99 (22)
[46]   Class of quantum many-body states that can be efficiently simulated [J].
Vidal, G. .
PHYSICAL REVIEW LETTERS, 2008, 101 (11)
[47]   Iterative quantum-classical path integral with dynamically consistent state hopping [J].
Walters, Peter L. ;
Makri, Nancy .
JOURNAL OF CHEMICAL PHYSICS, 2016, 144 (04)
[48]   Quantum-classical path integral with a harmonic treatment of the back-reaction [J].
Wang, Fei ;
Makri, Nancy .
JOURNAL OF CHEMICAL PHYSICS, 2019, 150 (18)
[49]   Multilayer formulation of the multiconfiguration time-dependent Hartree theory [J].
Wang, HB ;
Thoss, M .
JOURNAL OF CHEMICAL PHYSICS, 2003, 119 (03) :1289-1299
[50]   DENSITY-MATRIX FORMULATION FOR QUANTUM RENORMALIZATION-GROUPS [J].
WHITE, SR .
PHYSICAL REVIEW LETTERS, 1992, 69 (19) :2863-2866