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arXiv:1511.01501 · Physical review. B./Physical review. B

Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states

A. Honecker, Stefan Weßel, René John Kerkdyk, Thomas Pruschke, Frédéric Mila, Bruce Normand

Published Feb 8, 2016• 48 citations
arXivHTMLPDF

Abstract

Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg $S=\frac{1}{2}$ spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of $L=200$ ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multiparticle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.

DOI
10.1103/physrevb.93.054408

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Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg S=12S=\frac{1}{2}S=21​ spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of L=200L=200L=200 ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multiparticle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.
Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung by the infamous “sign problem.” Here we exploit the fact that the sign problem is basis-dependent. Recent studies have shown that passing to a dimer (two-site) basis eliminates the sign problem completely for a fully frustrated spin model on the two-leg ladder. We generalize this result to all partially frustrated two-leg spin-1/2 ladders, meaning those where the diagonal and leg couplings take any antiferromagnetic values. We find that, although the sign problem does reappear, it remains remarkably mild throughout the entire phase diagram. We explain this result and apply it to perform efficient quantum Monte Carlo simulations of frustrated ladders, obtaining accurate results for thermodynamic quantities such as the magnetic specific heat and susceptibility of ladders up to L = 200 L = 200 rungs (400 spins 1/2) and down to very low temperatures.
Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​ show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist all the way to infinite temperature. Our results offer valuable insight into the physics of finite-temperature spectral functions in SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​ and many other highly frustrated spin systems.
A two-leg quenched random bond disordered antiferromagnetic spin-1/2 Heisenberg ladder system is investigated by means of stochastic series expansion quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat, and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat takes the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/21/21/2 ladder, and a two-legged spin-1/21/21/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ\mathrm{XXZ}XXZ spin-1/21/21/2 chain in a magnetic field; the second-order terms give corrections to the XXZ\mathrm{XXZ}XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
Abstract In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( r=0r=0r=0 r = 0 ) case up to the diluted ( r→1r \rightarrow 1r→1 r → 1 ) limit, and for selected choices of number of legs LyL_yLy​ L y per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing LyL_yLy​ L y . Graphical Abstract
This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of strong coupling ladder compounds. For this class of compounds the rung coupling J ⊥ is much stronger than the coupling J ∥ along the ladder legs. The ground state properties of the integrable two-leg spin- and the mixed spin-() ladder models at zero temperature are analysed by means of the Thermodynamic Bethe Ansatz (TBA). Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are discussed in terms of the recently introduced High Temperature Expansion (HTE) method, which is reviewed in detail. In the strong coupling region the integrable spin- ladder model exhibits three quantum phases: (i) a gapped phase in the regime , (ii) a fully polarized phase for , and (iii) a Luttinger liquid magnetic phase in the regime H c1<H<H c2. The critical behaviour in the vicinity of the critical points H c1 and H c2 is of Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for the strong coupling ladder compounds (5IAP)2CuBr4· 2H2O, Cu2(C5H12N2)2Cl4, (C5H12N)2CuBr4, BIP-BNO and [Cu2(C2\O 2)(C10H8N2)2)](NO3)2. Similar analysis of the mixed spin-() ladder model reveals a rich phase diagram, with a and a full saturation magnetization plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetization plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetization curve obtained from the exact result derived from the TBA and HTE. The results are applied to the mixed ferrimagnetic ladder compound PNNBNO. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also discussed. For this model single-ion anisotropy can trigger different quantum phase transitions within the spin and orbital degrees of freedom, with magnetization plateaux arising from different spin and orbit Landé g-factors.