A computer code for topological quantum spin systems over triangulated surfaces

We derive explicit closed-form matrix representations of Hamiltonians drawn from tensored algebras, such as quantum spin Hamiltonians. These formulas enable us to soft-code generic Hamiltonian systems and to systematize the input data for uniformly structured as well as for un-structured Hamiltonians. The result is an optimal computer code that can be used as a black box that takes in certain input files and returns spectral information about the Hamiltonian. The code is tested on Kitaev’s toric model deployed on triangulated surfaces of genus 0 and 1. The efficiency of our code enables these simulations to be performed on an ordinary laptop. The input file corresponding to the minimal triangulation of genus 2 is also supplied.

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Marshall-positiveSU(N)quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians

Physical Review B ◽

10.1103/physrevb.91.054413 ◽

2015 ◽

Vol 91 (5) ◽

Cited By ~ 7

Author(s):

Ribhu K. Kaul

Keyword(s):

Quantum Spin ◽

Spin Systems ◽

Quantum Spin Systems ◽

Spin Hamiltonians ◽

Practical Strategy ◽

Sign Problem

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Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

Annales Henri Poincaré ◽

10.1007/s00023-021-01086-5 ◽

2021 ◽

Author(s):

Bruno Nachtergaele ◽

Robert Sims ◽

Amanda Young

Keyword(s):

Boundary Conditions ◽

Ground State ◽

Broad Class ◽

Sufficient Conditions ◽

Discrete Symmetry ◽

Quantum Spin ◽

Spontaneous Breaking ◽

Quantum Spin Systems ◽

Spin Models ◽

Topological Quantum

AbstractWe study the stability with respect to a broad class of perturbations of gapped ground-state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the Bravyi–Hastings–Michalakis (BHM) strategy that under a condition of local topological quantum order (LTQO), the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential. Compared to previous work, we expand the class of frustration-free quantum spin models that can be handled to include models with more general boundary conditions, and models with discrete symmetry breaking. Detailed estimates allow us to formulate sufficient conditions for the validity of positive lower bounds for the gap that are uniform in the system size and that are explicit to some degree. We provide a survey of the BHM strategy following the approach of Michalakis and Zwolak, with alterations introduced to accommodate more general than just periodic boundary conditions and more general lattices. We express the fundamental condition known as LTQO by means of an indistinguishability radius, which we introduce. Using the uniform finite-volume results, we then proceed to study the thermodynamic limit. We first study the case of a unique limiting ground state and then also consider models with spontaneous breaking of a discrete symmetry. In the latter case, LTQO cannot hold for all local observables. However, for perturbations that preserve the symmetry, we show stability of the gap and the structure of the broken symmetry phases. We prove that the GNS Hamiltonian associated with each pure state has a non-zero spectral gap above the ground state.

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Giant phonon anomalies in the proximate Kitaev quantum spin liquid α-RuCl3

Nature Communications ◽

10.1038/s41467-021-23826-1 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Haoxiang Li ◽

T. T. Zhang ◽

A. Said ◽

G. Fabbris ◽

D. G. Mazzone ◽

...

Keyword(s):

Acoustic Phonon ◽

Energy Scale ◽

Quantum Spin ◽

Majorana Fermion ◽

Spin Liquid ◽

Optical Phonons ◽

Large Intensity ◽

Topological Quantum ◽

Topological State ◽

Quantum Spin Liquid

AbstractThe Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we detect anomalous phonon effects in α-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. These phonon anomalies signify the coupling of phonon and Kitaev magnetic excitations in α-RuCl3 and demonstrates a proof-of-principle method to detect anomalous excitations in topological quantum materials.

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