Temperature dependence of energy transport in the chiral clock model
arXiv:2311.00046 · doi:10.1103/PhysRevB.109.235104
Abstract
We employ matrix product state simulations to study energy transport within the non-integrable regime of the one-dimensional chiral clock model. To induce a non-equilibrium steady state throughout the system, we consider open system dynamics with boundary driving featuring jump operators with adjustable temperature and footprint in the system. Given a steady state, we diagnose the effective local temperature by minimizing the trace distance between the true local state and the local state of a uniform thermal ensemble. Via a scaling analysis, we extract the transport coefficients of the model at relatively high temperatures above both its gapless and gapped low-temperature phases. In the medium-to-high temperature regime we consider, diffusive transport is observed regardless of the low-temperature physics. We calculate the temperature dependence of the energy diffusion constant as a function of model parameters, including in the regime where the model is quantum critical at the low temperature. Notably, even within the gapless regime, an analysis based on power series expansion implies that intermediate-temperature transport can be accessed within a relatively confined setup. Although we are not yet able to reach temperatures where quantum critical scaling would be observed, our approach is able to access the transport properties of the model over a broad range of temperatures and parameters. We conclude by discussing the limitations of our method and potential extensions that could expand its scope, for example, to even lower temperatures.
arXiv commentPublished version, 10+3 pages, 4+2 figures
References in corpus (59)
- The density-matrix renormalization group in the age of matrix product states
- Probing many-body dynamics on a 51-atom quantum simulator
- Efficient classical simulation of slightly entangled quantum computations
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Efficient simulation of one-dimensional quantum many-body systems
- Real time evolution using the density matrix renormalization group
- Matrix Product Density Operators: Simulation of finite-T and dissipative systems
- Time-dependent variational principle for quantum lattices
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Time-evolution methods for matrix-product states
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Random Quantum Circuits
- Finite-temperature transport in one-dimensional quantum lattice models
- A Universal Operator Growth Hypothesis
- Exact nonequilibrium steady state of a strongly driven open XXZ chain
- Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
- Algebraic versus exponential decoherence in dissipative many-particle systems
- Matrix product simulations of non-equilibrium steady states of quantum spin chains
- Simulation methods for open quantum many-body systems
- Operator space entanglement entropy in transverse Ising chain
- Relaxation times of dissipative many-body quantum systems
- Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
- Spectral theorem for the Lindblad equation for quadratic open fermionic systems
- Locality of temperature
- Quantum dynamics of thermalizing systems
- Influence of dephasing on many-body localization
- Numerical study of the chiral quantum phase transition in one spatial dimension
- Accessing scrambling using matrix product operators
- Exact Nonequilibrium Steady State of an Open Hubbard Chain
- Existence of temperature on the nanoscale
- Quantum field theory for the chiral clock transition in one spatial dimension
- Universal relaxational dynamics of gapped one dimensional models in the quantum sine-Gordon universality class
- Diffusive high-temperature transport in the one-dimensional Hubbard model
- Thermalization and ergodicity in many-body open quantum systems
- Phase diagram of the Parafermionic Chain with Chiral Interactions
- Product Spectrum Ansatz and the Simplicity of Thermal States
- On the uniqueness of the steady-state solution of the Lindblad-Gorini-Kossakowski-Sudarshan equation
- Energy transport in an integrable parafermionic chain via generalized hydrodynamics
- Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain
- Minimal length scales for the existence of local temperature
- Exact nonequilibrium steady state of open XXZ/XYZ spin-1/2 chain with Dirichlet boundary conditions
- Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
- Thermalization in Open Quantum Systems
- Coexistence of energy diffusion and local thermalization in nonequilibrium XXZ spin chains with integrability breaking
- Construction of Modular Branching Functions from Bethe's Equations in the 3-State Potts Chain
- Obtaining pure steady states in nonequilibrium quantum systems with strong dissipative couplings
- Nonequilibrium steady-state Kubo formula: equality of transport coefficients
- Measurable Consequences of the Local Breakdown of the Concept of Temperature
- Local temperature in quantum thermal states
- Temperature Dependent Energy Diffusion in Chaotic Spin Chains
- Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model
- The challenge of the chiral Potts model
- Thermodynamics of the 3-State Potts Spin Chain
- Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
- Thermal Drude weight in an integrable chiral clock model