Matrix Product State Representation without explicit local Hilbert Space Truncation with Applications to the Sub-Ohmic Spin-Boson Model

TL;DR

This paper introduces a novel matrix product state representation that avoids local Hilbert space truncation, enabling more accurate analysis of the sub-Ohmic spin-boson model and its quantum phase transition.

Contribution

The authors develop an alternative MPS method that bypasses local Hilbert space truncation, improving the study of spin-boson models and quantum phase transitions.

Findings

Successfully reproduce the critical exponent 1/2 of the phase transition

Determine infinite-chain critical couplings through extrapolation

Study system behavior deep into the localized phase

Abstract

We present an alternative to the conventional matrix product state representation, which allows us to avoid the explicit local Hilbert space truncation many numerical methods employ. Utilising chain mappings corresponding to linear and logarithmic discretizations of the spin-boson model onto a semi-infinite chain, we apply the new method to the sub-ohmic SBM. We are able to reproduce many well-established features of the quantum phase transition, such as the critical exponent 1/2 predicted by mean-field theory. Via extrapolation of finite-chain results, we are able to determine the infinite-chain critical couplings at which the transition occurs and, in general, study the behaviour of the system well into the localised phase.