Note on the thermodynamic Bethe Ansatz approach to the quantum phase diagram of the strong coupling ladder compounds

Abstract

We investigate the low-temperature phase diagram of the exactly solved su(4) two-leg spin ladder as a function of the rung coupling $J_{\perp }$ and magnetic field $H$ by means of the thermodynamic Bethe Ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H < H_{c1}, a fully polarized gapped phase for H > H_{c2} and a Luttinger liquid magnetic phase in the regime H_{c1} < H < H_{c2}. The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H_{c1} and H_{c2}, which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP)_2CuBr_4 2H_2 O, Cu_2(C_5 H_{12} N_2)_2 Cl_4 and (C_5 H_{12} N)_2 CuBr_4. In addition we predict the spin gap $\Delta \approx J_{\perp }-1/2J_{\parallel }$ for the weak coupling compounds with $J_{\perp }\sim J_{\parallel }$, such as (VO)_2 P_2 O_7, and also show that the gap opens for arbitrary $J_{\perp }/J_{\parallel }$.

arXiv comment10 pages, 3 figures

References in corpus (26)

• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• Experiments on Ladders Reveal a Complex Interplay between a Spin-Gapped Normal State and Superconductivity
• Coupled Ladders in a Magnetic Field
• Thermodynamics and spin gap of the Heisenberg ladder calculated by the look-ahead Lanczos algorithm
• The susceptibility and excitation spectrum of (VO)${}_2$P${}_2$O${}_7$ in ladder and dimer chain models
• One-dimensional spin-liquid without magnon excitations
• The Magnetic Spin Ladder (C_{5}H_{12}N)_{2}CuBr_{4}: High Field Magnetization and Scaling Near Quantum Criticality
• Non-Haldane Spin Liquid Models with Exact Ground States
• Zero Temperature Phase Transition in Spin-ladders: Phase Diagram and Dynamical studies of Cu(Hp)Cl
• NMR study of the S=1/2 Heisenberg Ladder Cu2(C5H12N2)2Cl4 : Quantum phase transition and critical dynamics
• Strong Coupling Expansions for Antiferromagnetic Heisenberg S=1/2 Ladders
• Magnetic properties of a new molecular-based spin-ladder system: (5IAP)2CuBr4*2H2O
• Exact solution of a spin-ladder model
• Identification of Nuclear Relaxation Processes in a Gapped Quantum Magnet: Proton NMR in the S=1/2 Heisenberg Ladder Cu2(C5H12N2)2Cl4
• The Magnetization of Cu_2(C_5H_{12}N_2)_2Cl_4 : A Heisenberg Spin Ladder System
• Integrable Magnetic Model of Two Chains Coupled by Four-Body Interactions
• Exactly solvable quantum spin tubes and ladders
• Field Dependence of the Magnetization for the spin-ladder material Cu_2(C_5H_{12}N_2)_2Cl_4
• Integrable Chain Model with Additional Staggered Model Parameter
• Theoretical analysis of the experiments on the double-spin-chain compound -- KCuCl${}_3$
• Phase diagram of the su(8) quantum spin tube
• Magnetization Plateaus in a Solvable 3-Leg Spin Ladder
• Phase diagram of an exactly solvable t-J ladder model
• Staggered Anisotropy Parameter Modification of the Anisotropic $t-J$ Model
• Exactly solvable su(N) mixed spin ladders
• Magnetization Plateaux in Bethe Ansatz Solvable Spin-S Ladders

Cited by in corpus (11)

• Superuniversality of superdiffusion
• Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds
• Exact results for the thermal and magnetic properties of strong coupling ladder compounds
• Thermal and magnetic properties of spin-1 magnetic chain compounds with large single-ion and in-plane anisotropies
• Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model
• Thermal and magnetic properties of integrable spin-1 and spin-3/2 chains with applications to real compounds
• Thermodynamic properties of an integrable quantum spin ladder with boundary impurities
• Quantum phase diagram of an exactly solved mixed spin ladder
• Exact solution and magnetic properties of an anisotropic spin ladder
• Quantum state transfer using 1D Heisenberg Hamiltonian on quasi-1D lattices
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit