Thermodynamics of dilute XX chain in a field

TL;DR

This paper provides an exact analytical study of the thermodynamics of a dilute XX spin chain in a magnetic field, revealing quantum phase transitions characterized by magnetization jumps and their effects on thermodynamic properties.

Contribution

It introduces a detailed analytical description of the thermodynamics of dilute XX chains, highlighting the impact of dilution-induced quantum phase transitions.

Findings

Quantum phase transitions with magnetization jumps occur in dilute XX chains.

Thermodynamic quantities like magnetization, entropy, and susceptibility show distinctive behavior at transitions.

Dilution significantly alters the correlation functions and low-temperature properties.

Abstract

The isotropic spin one-half XY chain in transverse field (XX chain) has specific ground state phase with permanent criticality (quasi-long-range ordered, QLRO, phase) which exists in a field less than nearest-neighbor exchange. It is characterized by gapless excitations and power law decay of transverse correlators. The dilution of XX chain has drastic effect on this phase: the infinite series of quantum phase transitions marked by magnetization jumps appears in it. The thermodynamics of dilute XX chain allows exact analytical description revealing the peculiarities of the appearing transitions. We calculate the low-temperature magnetization, entropy, longitudinal magnetic susceptibility and specific heat of dilute model to elucidate the influence of quantum transitions on their field and low-temperature behavior. The changes of pair spin correlators under dilution are also analyzed. We argue that other dilute quantum spin chains and ladders with the gapless (algebraic) spin-liquid states would also exhibit the quantum jumps under variation of couplings and field similar to those of XX chain.