Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution

Binder, Moritz; Barthel, Thomas

doi:10.1103/physrevb.92.125119

Cited by 41 publications

(43 citation statements)

References 47 publications

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“…Two possible choices exist within the MPS framework: minimally entangled typical thermal states [64] and thermofield doublet states [8,65,66]. In the following, we will concentrate on thermofield doublet states or "purifications" of a mixed state; a detailed comparison between both methods can be found in [51]. The purification works by doubling the Hilbert space H → H p ⊗ H a where a denotes the auxiliary or ancilla degrees of freedom.…”

Section: Finite Temperaturesmentioning

confidence: 99%

Time-evolution methods for matrix-product states

et al. 2019

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Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W I,II method, the global Krylov method, the local Krylov method and the one-and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

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Section: Finite Temperaturesmentioning

confidence: 99%

Time-evolution methods for matrix-product states

et al. 2019

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“…We use the ITensor library for these calculations [71]. To address the challenge of mixed states (finite temperature), many MPS-based methods have been proposed, developed, and compared [72], e.g., the finite-temperature Lanczos method [73], the purification scheme of a pure state in an enlarged Hilbert space [74], and, more recently, the minimally-entangled typically thermal states approach [75,76]. In this paper, we use the purification scheme which introduces an auxiliary Hilbert space Q acting as a thermal bath.…”

Section: Matrix Product Statesmentioning

confidence: 99%

Dynamical properties of the S=12 random Heisenberg chain

et al. 2018

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We study dynamical properties at finite temperature (T ) of Heisenberg spin chains with random antiferrormagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor S(q, ω) and its ω → 0 limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate 1/T1). Our study reveals a continuous narrow band of low-energy excitations in S(q, ω), extending throughout the q-space, instead of being restricted to q ≈ 0 and q ≈ π as found in the uniform system. Close to q = π, the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted q-dependence further away from q = π. Furthermore we also find spin diffusion effects close to q = 0 that are not contained within the random-singlet theory but give non-negligible contributions to the mean 1/T1. To compare with NMR experiments, we consider the distribution of the local relaxation rates 1/T1. We show that the local 1/T1 values are broadly distributed, approximately according to a stretched exponential. The mean 1/T1 first decreases with T , but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ω0. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean 1/T1 has never been experimentally observed. Indeed, we show that the divergence of the mean 1/T1 is due to rare events in the disordered chains and is concealed in experiments, where the typical 1/T1 value is accessed. *

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“…Note that the trick of Eq. (4), in a generalized form, also works for non-zero temperatures [32][33][34]. Another device to reach longer times, which is by now a standard tool, is to extrapolate the simulation data through linear prediction [35,36].…”

Section: Response Functions For Translation-invariant Systemsmentioning

confidence: 99%

Infinite boundary conditions for response functions and limit cycles within the infinite-system density matrix renormalization group approach demonstrated for bilinear-biquadratic spin-1 chains

Binder

Barthel

2018

Phys. Rev. B

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Response functions Ax(t)By(0) for one-dimensional strongly correlated quantum many-body systems can be computed with matrix product state (MPS) techniques. Especially, when one is interested in spectral functions or dynamic structure factors of translation-invariant systems, the response for some range |x − y| < is needed. We demonstrate how the number of required time-evolution runs can be reduced substantially: (a) If finite-system simulations are employed, the number of time-evolution runs can be reduced from to 2 √ . (b) To go beyond, one can employ infinite MPS (iMPS) such that two evolution runs suffice. To this purpose, iMPS that are heterogeneous only around the causal cone of the perturbation are evolved in time, i.e., the simulation is done with infinite boundary conditions. Computing overlaps of these states, spatially shifted relative to each other, yields the response functions for all distances |x−y|. As a specific application, we compute the dynamic structure factor for ground states of bilinear-biquadratic spin-1 chains with very high resolution and explain the underlying low-energy physics. To determine the initial uniform iMPS for such simulations, infinite-system density-matrix renormalization group (iDMRG) can be employed. We discuss that, depending on the system and chosen bond dimension, iDMRG with a cell size nc may converge to a non-trivial limit cycle of length m. This then corresponds to an iMPS with an enlarged unit cell of size mnc. arXiv:1804.09163v2 [cond-mat.str-el]

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Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution

Cited by 41 publications

References 47 publications

Time-evolution methods for matrix-product states

Time-evolution methods for matrix-product states

Dynamical properties of the S=12 random Heisenberg chain

Infinite boundary conditions for response functions and limit cycles within the infinite-system density matrix renormalization group approach demonstrated for bilinear-biquadratic spin-1 chains

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