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Transport and dynamics of low-dimensional quantum spin systems

Yousef Rahnavard

Published Jul 29, 2014• 0 citations
Publisher

Abstract

In this thesis, I use a quantum Monte Carlo (QMC) method based on the stochastic series expansion (SSE) to study transport, quantum phase diagrams, and dynamics of several one- and quasi-one-dimensional spin systems, including spin-1/2 and spin-1 chains, a frustrated four-leg spin tube, and N-leg spin-1/2 ladders. I establish a diffusive channel for the finite temperature spin transport of the spin-1/2 antiferromagnetic Heisenberg chain. Extensive finite size studies are detailed, allowing to extract the diffusion kernel in the thermodynamic limit. The diffusion is found to exhibit no anomalous exponent, moreover it is shown to survive for finite values of exchange anisotropy and magnetic fields, however with a strong suppression away from the isotropic point and for increasing magnetic fields. In the case of the spin-1 chain, I obtain the quantum phase diagram and spin dynamics in the combined presence of finite single-ion anisotropies and external magnetic fields. I also prove the existence of magnon modes and multi-particle continua and determine their evolutions as a function of anisotropies and magnetic fields. Moreover, I calculate the magnetic field dependence of the nuclear magnetic relaxation as a function of the single ion anisotropy. For the quasi-one-dimensional spin system of a frustrated four-leg tube, I investigate the regime of large rung coupling, where QMC is applicable. I evaluate the uniform spin susceptibility and the dynamic structure factor and show that in this regime the spin-tube exhibts a crossover from a gapped effective antiferromagnetic spin-2 chain behavior with massive magnons to a gapless Luttinger liquid phase with spinon excitations. Finally, I investigate the spin dynamics of N-leg spin-1/2 ladders with spacially isotropic interactions for N=1,..,5. I obtain the low-lying excitations of the spin ladders as a function of the number of legs and show that they exhibt an even-odd oscillation which is consistent with Haldane's conjecture and other known results for the thermodynamics of spin ladders.

DOI
10.24355/dbbs.084-201408291011-1

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In this thesis, I use a quantum Monte Carlo (QMC) method based on the stochastic series expansion (SSE) to study transport, quantum phase diagrams, and dynamics of several one- and quasi-one-dimensional spin systems, including spin-1/2 and spin-1 chains, a frustrated four-leg spin tube, and N-leg spin-1/2 ladders. I establish a diffusive channel for the finite temperature spin transport of the spin-1/2 antiferromagnetic Heisenberg chain. Extensive finite size studies are detailed, allowing to extract the diffusion kernel in the thermodynamic limit. The diffusion is found to exhibit no anomalous exponent, moreover it is shown to survive for finite values of exchange anisotropy and magnetic fields, however with a strong suppression away from the isotropic point and for increasing magnetic fields. In the case of the spin-1 chain, I obtain the quantum phase diagram and spin dynamics in the combined presence of finite single-ion anisotropies and external magnetic fields. I also prove the existence of magnon modes and multi-particle continua and determine their evolutions as a function of anisotropies and magnetic fields. Moreover, I calculate the magnetic field dependence of the nuclear magnetic relaxation as a function of the single ion anisotropy. For the quasi-one-dimensional spin system of a frustrated four-leg tube, I investigate the regime of large rung coupling, where QMC is applicable. I evaluate the uniform spin susceptibility and the dynamic structure factor and show that in this regime the spin-tube exhibts a crossover from a gapped effective antiferromagnetic spin-2 chain behavior with massive magnons to a gapless Luttinger liquid phase with spinon excitations. Finally, I investigate the spin dynamics of N-leg spin-1/2 ladders with spacially isotropic interactions for N=1,..,5. I obtain the low-lying excitations of the spin ladders as a function of the number of legs and show that they exhibt an even-odd oscillation which is consistent with Haldane's conjecture and other known results for the thermodynamics of spin ladders.
This PhD thesis concerns the physics of low-dimensional quantum systems and especially quantum spin ladders. Novel metal-organic compounds (C5H12N)2CuBr4 and (C5H12N)2CuCl4 are investigated as model materials for low-dimensional quantum behavior by neutron scattering experiments and by measurements of magnetic and thermodynamic properties. The experimental results are compared quantitatively to calculations using a variety of theoretical and numerical methods (DMRG, ED) of the ground state and excitations of such systems. Key results are the determination of the Hamiltonian and its exchange parameters of (C5H12N)2CuCl4 studied here for the first time from quantitative modelling of magnetic susceptibility and neutron spectroscopy data. When a magnetic field is applied two quantum critical points occur at which fractionalization of the elementary quasi-particle excitations is ob- served. The characteristic excitation continua are explained by effective spin-chain and t-J models and are observed systematically as a function of magnetic field and temperature. Coherent and incoherent spin Luttinger-liquid physics is observed and for the first time modelled fully quantitatively. The chemical flexibility of the these metal-organic compounds allows continuous solid-state mixtures of Br and Cl resulting in systems with quenched disorder. The rung and leg exchange parameters assume discrete values given by the specific chemical composition of the exchange pathways. The influence of such quenched disorder on the excitations of quantum spin ladders has been studied experimentally. The observed spectra with damped excitations of the unperturbed ladder and more localized modes provide detailed insights into the physics that may be observed in such systems if a magnetic field is applied and so called Bose glass phases are induced.
In this thesis I present a theoretical study of three different\nstrongly correlated systems: Luttinger liquids, spin-1 chains and\nthe two-dimensional spin-1/2 Heisenberg model.\n\nFor every sub-field of our research I summarize the background and\nprovide further details to the work presented in the appended\npapers. Chapter 1 corresponds to paper I, Chapter 2 to paper II,\nChapter 3 and 4 to paper III and IV.\n\nIn paper I, we calculate with bosonization techniques the local\ndensity of states of a finite segment of Luttinger liquid. Besides of\nbeing of experimental relevance for Scanning Tunneling Microscopy\nexperiments on carbon nanotubes and cleaved overgrowth wires, the\nwave functions of a "Luttinger liquid in a box" very nicely\nvisualize the fundamental bosonic nature of the low energy\nexcitations.\n\nIn paper II, we analyze with field theory methods how the presence\nof a single-ion anisotropy affects the behavior of a spin-1 chain.\nWe determine in the framework of the Non Linear Sigma Model how the gaps\nof the anisotropic chain depend on an applied staggered magnetic\nfield. Our theoretical analysis is meant to model compounds like\nrmR2BaNiO5\\rm R_2BaNiO_5rmR2​BaNiO5​ that show coexistence of Haldane phase and\nlong-range order.\n\nIn paper III, we compute with quantum Monte Carlo simulations the\nlocal response to a uniform magnetic field around vacancies in the\ntwo-dimensional Heisenberg model. From the full understanding of the\nnumerical results, we can make quantitative predictions of relevance\nfor Nuclear Magnetic Resonance and susceptibility experiments. In\nparticular, we expect, even in the thermodynamic limit, a finite\nCurie contribution to the total susceptibility arising from the\nimpurities.\n\nFinally in paper IV, we consider interaction effects among\nimpurities. We compute the potential between static vacancies in\nseveral low-dimensional spin-1/2 antiferromagnets comparing\nthe numerics with exact results from conformal field theory and\nlinear spin wave theory. The potential is directly related to the\nlocal valence bond order and its magnitude is a loyal measure of the\namount of quantum correlations present into the system.
Using large-scale determinant quantum Monte Carlo simulations in combination with the stochastic analytical continuation, we study two-particle dynamical correlation functions in the anisotropic square lattice of weakly coupled one-dimensional (1D) Hubbard chains at half filling and in the presence of weak frustration. The evolution of the static spin structure factor upon increasing the interchain coupling is suggestive of the transition from the power-law decay of spin-spin correlations in the 1D limit to long-range antiferromagnetic order in the quasi-1D regime and at T=0T=0T=0. In the numerically accessible regime of interchain couplings, the charge sector remains gapped. The low-energy momentum dependence of the spin excitations is well described by the linear spin-wave theory with the largest intensity located around the antiferromagnetic wave vector. This magnon mode corresponds to a bound state of two spinons. At higher energies the spinons deconfine and we observe signatures of the two-spinon continuum which progressively fade away as a function of interchain hopping.
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.
By means of nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\ensuremath{-}}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system (C5H12N)2CuBr4({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}(C5​H12​N)2​CuBr4​. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{\ensuremath{-}1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{\ensuremath{-}1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.
This thesis is dedicated to the analytical and numerical study of quantum entanglement and nonlocality in strongly correlated quantum spin tube models in connection with various thermodynamic properties and magnetization processes. More specifically, the study builds on the analysis of the behavior of these physical quantities within a particular spinning network that includes competitive interactions and quantum fluctuations known as a three-leg spins ladder or triangular spin tube, due to the periodic boundary conditions imposed on the three spins that form the Heisenberg steps of this network. In systems with this structure described above, magnetization plateaus are formed due to the competition imposed by the geometric frustration that the network imposes on the spins and the applied external field. Such competition is the mechanism that defines the orientation of the magnetic domains that the network will present, which within specific regions of the network parameters space create regions where there is a discontinuous response of local magnetization to external field variations, such regions are known as magnetization plateaus. To evaluate the frustrated spin- ½ Ising-Heisenberg triangular tube consisting of a spin tube formed by triangular unit cells with 3 spins-½ interconnected by Heisenberg couplings between neighboring first spins and the pairs of neighboring first spins belonging to the different cells have their interaction intermediated through classical Ising couplings, an exact analytical procedure, known as a transfer-matrix technique, was used to obtain the analytical solutions for various thermodynamic properties of the model, including magnetization, specific heat and magnetization profiles. These quantities were evaluated as a function of temperature, external magnetic field and the relevant couplings. However, it was necessary to apply a different methodology to obtain thermodynamic measurements for the other model proposed in this thesis: the frustrated spin- ½ Heisenberg triangular tube, which consists of a spin tube with similar structure to the previous one, except that the pairs of the first neighboring spins belonging to the different cells interact through Heisenberg-type quantum connections. In this case, a numerical procedure known as the quantum density matrix renormalization group method, known as DMRG, is used to obtain the ground state diagrams, magnetization processes, and bipartite quantum entanglement of the Heisenberg triangular tubes as a function of the external magnetic field and the relevant couplings. In both models, the magnetization curves exhibit discontinuous magnetization jumps and intermediate plateaus due to discontinuous phase transitions induced by the external field, These transitions are also reflected in the exotic behavior of some thermodynamic quantities of the models, such as the presence of a striking low temperature peak for the specific heat curve and a highlighted magnetocaloric effect.