From Linear to Nonlinear Responses of Thermal Pure Quantum States

TL;DR

This paper introduces a self-validating method to compute linear and nonlinear responses of quantum many-body systems at any temperature, revealing rich excitation dynamics and nonlinear effects through time evolution of thermal pure states.

Contribution

It presents a novel formalism for unbiased response calculations using thermal pure quantum states, with rigorous error bounds and applications to complex magnetic systems.

Findings

Accurate response functions obtained with exponentially decreasing error bounds.

High-field nonlinear responses show band deformation in ferromagnetic chains.

Broad nonlinear peaks indicate complex quasi-particle collisions in kagome antiferromagnets.

Abstract

We propose a self-validating scheme to calculate the unbiased responses of quantum many-body systems to external fields of arbibraty strength at any temperature. By switching on a specified field to a thermal pure quantum state of an isolated system, and tracking its time evolution, one can observe an intrinsic thermalization process driven solely by many-body effects. The transient behavior before thermalization contains rich information on excited states, giving the linear and nonlinear response functions at all frequencies. We uncover the necessary conditions to clarify the applicability of this formalism, supported by a proper definition of the nonlinear response function. The accuracy of the protocol is guaranteed by a rigorous upper bound of error exponentially decreasing with system size, and is well implemented in the simple ferromagnetic Heisenberg chain, whose response at high fields exhibits a nonlinear band deformation. We further extract the characteristic features of excitation of the spin-1/2 kagome antiferromagnet; the wavenumber-insensitive linear responses from the possible spin liquid ground state, and the significantly broad nonlinear peaks which should be generated from numerous collisions of quasi-particles, that are beyond the perturbative description.