Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
SciPost Physics SciPost Foundation 12:1 (2022) 019
Abstract:We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following , provides a natural and unified framework for out-of-equilibrium physics in this model. We show that all correlation functions in the CE can be computed using form factor expansion and expressed in terms of Fredholm determinants. In particular, we present exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter 1-point function, dynamical 2-point function and equal-time 3-point function.
Duality between weak and strong interactions in quantum gases
Physical Review Letters American Physical Society 128:2 (2022) 021604
Abstract:In one-dimensional quantum gases there is a well known “duality” between hard core bosons and noninteracting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Here we propose a solution to this long-standing problem. Our derivation relies on regularizing the only pointlike interaction between fermions in one dimension that induces a discontinuity in the wave function proportional to its derivative. In contrast to all known regularizations our potential is weak for small interaction strengths. Crucially, this allows one to apply standard methods of diagrammatic perturbation theory to strongly interacting bosons. As a first application we compute the finite temperature spectral function of the Cheon-Shigehara model, the fermionic model dual to the celebrated Lieb-Liniger model.
A short introduction to Generalized Hydrodynamics
Physica A: Statistical Mechanics and its Applications (2022)
Abstract:These are notes based on lectures given at the 2021 summer school on Fundamental Problems in Statistical Physics XV. Their purpose is to give a very brief introduction to Generalized Hydrodynamics, which provides a description of the large scale structure of the dynamics in quantum integrable models. The notes are not meant to be comprehensive or provide an overview of all relevant literature, but rather give an exposition of the key ideas for non-experts, using a simple fermionic tight-binding model as the main example.
Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
Journal of Statistical Mechanics: Theory and Experiment IOP Publishing 2021 (2021) 103102
Abstract:We consider a Lindblad equation that for particular initial conditions reduces to an asymmetric simple exclusion process with additional loss and gain terms. The resulting Lindbladian exhibits operator-space fragmentation and each block is Yang–Baxter integrable. For particular loss/gain rates the model can be mapped to free fermions. We determine the full quantum dynamics for an initial product state in this case.
Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
SciPost Physics SciPost 11:3 (2021) 068