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arXiv:cond-mat/0309376 · Physical review. B, Condensed matter

Quantum Monte Carlo simulation for the conductance of one-dimensional quantum spin systems

Kim Louis, Claudius Gros

Published Nov 26, 2003• 17 citations
arXivHTMLPDF

Abstract

Recently, the stochastic series expansion (SSE) has been proposed as a powerful Monte Carlo method, which allows simulations at low T for quantum-spin systems. We show that the SSE allows us to compute the magnetic conductance for various one-dimensional spin systems without further approximations. We consider various modifications of the anisotropic Heisenberg chain. We recover the Kane-Fisher scaling for one impurity in a Luttinger liquid and study the influence of noninteracting leads for the conductance of an interacting system.

DOI
10.1103/physrevb.68.184424

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Recently, the stochastic series expansion (SSE) has been proposed as a powerful Monte Carlo method, which allows simulations at low T for quantum-spin systems. We show that the SSE allows us to compute the magnetic conductance for various one-dimensional spin systems without further approximations. We consider various modifications of the anisotropic Heisenberg chain. We recover the Kane-Fisher scaling for one impurity in a Luttinger liquid and study the influence of noninteracting leads for the conductance of an interacting system.
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We present results for the spin conductance of the one-dimensional spin-1∕21∕21∕2 Heisenberg and XYXYXY models coupled to phonons. We apply an approach based on the stochastic series expansion (quantum Monte Carlo) method to evaluate the conductance for a variety of phonon dispersions and values of spin-phonon coupling. From our numerical simulations and analytical arguments, we derive several scaling laws for the conductance.
In this paper we develop the stochastic cluster series expansion (SCSE) which is a (cluster) variant of the stochastic series expansion (SSE) method. For certain systems with longer-range interactions the SCSE is considerably more efficient than the standard implementation of the SSE, at low temperatures. As an application of this method we calculated the T=0T=0T=0 conductance for a linear Heisenberg chain with a (diagonal) next-nearest-neighbor interaction.
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.
We study electron and spin transport in interacting quantum wires contacted by noninteracting leads. We theoretically model the wire and junctions as an inhomogeneous chain where the parameters at the junction change on the scale of the lattice spacing. We study such systems analytically in the appropriate limits based on Luttinger liquid theory and compare the results to quantum Monte Carlo calculations of the conductances and local densities near the junction. We first consider an inhomogeneous spinless fermion model with a nearest-neighbor interaction and then generalize our results to a spinful model with an on-site Hubbard interaction.