Spin ladders and quantum simulators for Luttinger liquids

TL;DR

This paper investigates the magnetic insulator (Hpip)$_{2}$CuCl$_{4}$ as a quantum simulator for Luttinger liquids, determining its properties and exchange couplings to facilitate future studies on disorder effects in these systems.

Contribution

The study provides the first detailed analysis of (Hpip)$_{2}$CuCl$_{4}$'s exchange parameters and thermodynamic properties, establishing it as a platform for exploring disorder in Luttinger liquids.

Findings

Confirmed exchange parameters match experimental specific heat data.

Validated the Hamiltonian for (Hpip)$_{2}$CuCl$_{4}$.

Established a basis for future disorder effect studies.

Abstract

Magnetic insulators have proven to be usable as quantum simulators for itinerant interacting quantum systems. In particular the compound (C$_{5}$H$_{12}$N)$_{2}$CuBr$_{4}$ (short (Hpip)$_{2}$CuBr$_{4}$) was shown to be a remarkable realization of a Tomonaga-Luttinger liquid (TLL) and allowed to quantitatively test the TLL theory. Substitution weakly disorders this class of compounds and allows thus to use them to tackle questions pertaining to the effect of disorder in TLL as well, such as the formation of the Bose glass. As a first step in this direction we present in this paper a study of the properties of the related (Hpip)$_{2}$CuCl$_{4}$ compound. We determine the exchange couplings and compute the temperature and magnetic field dependence of the specific heat, using a finite temperature Density Matrix Renormalization group (DMRG) procedure. Comparison with the measured specific heat at zero magnetic field confirms the exchange parameters and Hamiltonian for the (Hpip)$_{2}$CuCl$_{4}$ compound, giving the basis needed to start studying the disorder effects.