Charge-density-wave melting in the one-dimensional Holstein model

Abstract

We study the Holstein model of spinless fermions, which at half filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the realtime evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photo induced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state densitymatrix renormalization group method for electron-phonon systems using local basis optimization.In our examples, we account for up to M ph = 40 bare phonons per site by working with O(10) optimal phonon modes.

Finite-temperature transport in one-dimensional quantum lattice models

“…An open question is the applicability of wave-function based methods to the study of transport in spin-phonon systems. Recent advances with DMRG methods using optimized local phonon basis (Zhang et al, 1998) already give access to real-time dynamics in electron-phonon systems (Brockt et al, 2015;Dorfner et al, 2015;Guo et al, 2012;Kloss et al, 2019;Stolpp et al, 2020), calling for extensions to finite temperatures and spin-phonon systems.…”

Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

“…A. Now, we consider the 1RDM, which is the central object of the LBO method [13,40,42]. The expectation value of the local density operators in the original Hilbert space can be written in terms of the 1RDMρ…”

“…Another typical problem featuring large local Hilbert spaces is the interplay between lattice fermions and phonons. For instance, the formation and stability of (Bi-)Polarons is a central problem and considerable effort has been taken for its investigation [6][7][8][9][10][11][12][13][14][15]. A broad class of different methods such as quantum Monte Carlo [16,17], density-functional theory [18], density-matrix embedding theory [19], or dynamical mean-field theory [20][21][22] has been explored to study its various aspects.…”

“…In order to overcome such restrictions, approaches such as the pseudo site (PS) and the local-basis optimization (LBO) method [6,[40][41][42] were developed. These methods have proven to be successful tools for treating fermion-phonon couplings in the Holstein model, even out of equilibrium and at finite temperature [6,10,13,14].…”

Report on scipost_202009_00002v1

“…Another typical problem featuring large local Hilbert spaces is the interplay between lattice fermions and phonons. For instance, the formation and stability of (Bi-)Polarons is a central problem and considerable effort has been taken for its investigation [6][7][8][9][10][11][12][13][14][15]. A broad class of different methods such as quantum Monte Carlo [16,17], density-functional theory [18], density-matrix embedding theory [19], or dynamical meanfield theory [20][21][22] has been explored to study its various aspects.…”