Schmidt gap in random spin chains

TL;DR

This paper studies the entanglement spectrum of random spin chains, showing that the Schmidt gap effectively identifies critical points and exhibits universal scaling behavior.

Contribution

It provides a numerical analysis of the Schmidt gap in two different disordered spin models, demonstrating its utility as a critical point detector and its universal scaling properties.

Findings

Schmidt gap accurately detects critical points

Schmidt gap scales with universal critical exponents

Analysis applies to both exactly solvable and numerical models

Abstract

We numerically investigate the low-lying entanglement spectrum of the ground state of random one-dimensional spin chains obtained after partition of the chain into two equal halves. We consider two paradigmatic models: the spin-1/2 random transverse field Ising model, solved exactly, and the spin-1 random Heisenberg model, simulated using the density matrix renormalization group. In both cases we analyze the mean Schmidt gap, defined as the difference between the two largest eigenvalues of the reduced density matrix of one of the two partitions, averaged over many disorder realizations. We find that the Schmidt gap detects the critical point very well and scales with universal critical exponents.