Spin ladders and quantum simulators for Luttinger liquids

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.

Part of the special issue "Physics in one dimension", A van Houselt, J Schäfer, H J W Zandvliet and R Claessen ed

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Bose-Einstein Condensation in Magnetic Insulators
• New Trends in Density Matrix Renormalization
• Controlling Luttinger liquid physics in spin ladders under a magnetic field
• Thermodynamics of the Spin Luttinger-Liquid in a Model Ladder Material
• Direct Observation of Magnon Fractionalization in the Quantum Spin Ladder
• Field-Controlled Magnetic Order in the Quantum Spin-Ladder System (Hpip)2CuBr4
• Anisotropy of Magnetic Interactions in the Spin-Ladder Compound (C${}_5$H${}_{12}$N)${}_2$CuBr${}_4$
• Density-matrix renormalization group methods for momentum- and frequency-resolved dynamical correlation functions

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• Temperature dependence of the NMR spin-lattice relaxation rate for spin-1/2 chains
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• Disorder-induced Revival of the Bose-Einstein Condensation in Ni(Cl${}_{1-x}$Br${}_x$)${}_2$-4SC(NH${}_2$)${}_2$ at High Magnetic Fields
• Impact of strong disorder on the static magnetic properties of the spin-chain compound BaCu2SiGeO7
• Magnetic field induced bound states in spin-$\frac{1}{2}$ ladders
• Finite temperature dynamical correlations for the dimerized spin-1/2 chain
• Thermodynamics of the spin-1/2 two-leg ladder compound $(C_5{H}_{12}N{)}_{2}CuB{r}_4$
• Fingerprints of supersymmetric spin and charge dynamics observed by inelastic neutron scattering
• Low dimensional correlations under thermal fluctuations
• Electron spin resonance study of spin relaxation in the strong-leg spin ladder with nonmagnetic dilution
• Field-induced ordering in a random-bond quantum spin ladder compound with weak anisotropy
• Magnetic and phononic dynamics in the two-ladder quantum magnet (C5H9NH3)2CuBr4