Investigation of Quantum Phase Transitions using Multi-target DMRG Methods

TL;DR

This paper explores how conformal invariance predictions can be used with multi-target DMRG methods, enhanced by Thick-restart Lanczos, to analyze quantum phase transitions, especially near critical points.

Contribution

It introduces a method combining conformal field theory with multi-target DMRG using Thick-restart Lanczos for accurate excited state targeting.

Findings

Successfully matched low-lying energy levels with conformal spectra

Demonstrated effectiveness on anisotropic spin-1 Hamiltonian

Provided a general approach for studying quantum critical phenomena

Abstract

In this paper we examine how the predictions of conformal invariance can be widely exploited to overcome the difficulties of the density-matrix renormalization group near quantum critical points. The main idea is to match the set of low-lying energy levels of the lattice Hamiltonian, as a function of the system's size, with the spectrum expected for a given conformal field theory in two dimensions. As in previous studies this procedure requires an accurate targeting of various excited states. Here we discuss how this can be achieved within the DMRG algorithm by means of the recently proposed Thick-restart Lanczos method. As a nontrivial benchmark we use an anisotropic spin-1 Hamiltonian with special attention to the transitions from the Haldane phase. Nonetheless, we think that this procedure could be generally valid in the study of quantum critical phenomena.