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Register a new userMicroscopic Study of the Halperin - Laughlin Interface through Matrix Product States
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Interfaces between topologically distinct phases of matter reveal a remarkably rich phenomenology. We study the experimentally relevant interface between a Laughlin phase at filling factor $ u=1/3$ and a Halperin 332 phase at filling factor $ u=2/5$. Based on our recent construction of chiral topological interfaces in [Nat. Commun. 10, 1860 (2019)], we study a family of model wavefunctions that captures both the bulk and interface properties. These model wavefunctions are built within the matrix product state framework. The validity of our approach is substantiated through extensive comparisons with exact diagonalization studies. We probe previously unreachable features of the low energy physics of the transition. We provide, amongst other things, the characterization of the interface gapless mode and the identification of the spin and charge excitations in the many-body spectrum. The methods and tools presented are applicable to a broad range of topological interfaces.
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We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density operators of translational invariant systems. The results give a theoretical justification for the high accuracy of renormalization group algorithms, and justifies their use even in the case of critical systems.
We use conformal field theory to construct model wavefunctions for a gapless interface between latti
We study geometric aspects of the Laughlin fractional quantum Hall (FQH) states using a description of these states in terms of a matrix quantum mechanics model known as the Chern-Simons matrix model (CSMM). This model was proposed by Polychronakos as a regularization of the noncommutative Chern-Simons theory description of the Laughlin states proposed earlier by Susskind. Both models can be understood as describing the electrons in a FQH state as forming a noncommutative fluid, i.e., a fluid occupying a noncommutative space. Here we revisit the CSMM in light of recent work on geometric response in the FQH effect, with the goal of determining whether the CSMM captures this aspect of the physics of the Laughlin states. For this model we compute the Hall viscosity, Hall conductance in a non-uniform electric field, and the Hall viscosity in the presence of anisotropy (or intrinsic geometry). Our calculations show that the CSMM captures the guiding center contribution to the known values of these quantities in the Laughlin states, but lacks the Landau orbit contribution. The interesting correlations in a Laughlin state are contained entirely in the guiding center part of the state/wave function, and so we conclude that the CSMM accurately describes the most important aspects of the physics of the Laughlin FQH states, including the Hall viscosity and other geometric properties of these states which are of current interest.
We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows to extend the density matrix renormalization group and variational matrix product state formalism to quantum field theories and continuum models in 1 spatial dimension. We illustrate our procedure with the Lieb-Liniger model.
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be applied to a wide variety of situations. As a first test, we show how it provides reliable results in the computation of fundamental properties of a chain of quantum harmonic oscillators achieving off-critical and critical relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use it to study the ground state properties of the quantum rotor model in one spatial dimension, a model that can be mapped to the Mott insulator limit of the 1-dimensional Bose-Hubbard model. At the quantum critical point, the central charge associated to the underlying conformal field theory can be computed with good accuracy by measuring the finite-size corrections of the ground state energy. Examples of MPS-computations both in the finite-size regime and in the thermodynamic limit are given. The precision of our results are found to be comparable to those previously encountered in the MPS studies of, for instance, quantum spin chains. Finally, we present a spin-off application: an iterative technique to efficiently get numerical solutions of partial differential equations of many variables. We illustrate this technique by solving Poisson-like equations with precisions of the order of 10^(-7).
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