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Title: Generalised route to effective field theories for quantum systems with local constraints

Abstract

Some of the exciting phenomena uncovered in strongly correlated systems in recent years – for instance quantum topological order, deconfined quantum criticality and emergent gauge symmetries – appear in systems where the Hilbert space is effectively projected at low energies in a way that imposes local constraints on the original degrees of freedom. Cases in point include spin liquids, valence bond systems, dimer and vertex models. In this work, we use a slave boson description coupled to a large-S path integral formulation to devise a generalised route to obtain effective field theories for such systems. We demonstrate the validity and capability of our approach by studying quantum dimer models and by comparing our results with the existing literature.Field theoretic approaches to date are limited to bipartite lattices, they depend on a gauge-symmetric under-standing of the constraint, and lack generic quantitative predictive power for the coefficients of the terms that appear in the Lagrangians of these systems. Our method overcomes all these shortcomings and we show how the results up to quadratic order compare with the known height description of the square lattice quantum dimer model, as well as with the numerical estimate of the speed of light of the photonmore » excitations on the diamond lattice. Lastly, instanton considerations allow us to infer properties of the finite temperature behaviour in two dimensions.« less

Authors:
 [1]; ORCiD logo [2];  [1];  [3]
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  1. Univ. of Cambridge, Cambridge (United Kingdom)
  2. Brookhaven National Lab. (BNL), Upton, NY (United States)
  3. Rutgers Univ., Piscataway, NJ (United States)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1530523
Alternate Identifier(s):
OSTI ID: 1547961
Report Number(s):
BNL-211810-2019-JAAM
Journal ID: ISSN 2469-9950; PRBMDO
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 100; Journal Issue: 8; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Szabo, Attila, Tsvelik, Alexei M., Castelnovo, Claudio, and Goldstein, Garry. Generalised route to effective field theories for quantum systems with local constraints. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.100.085113.
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Szabo, Attila, Tsvelik, Alexei M., Castelnovo, Claudio, & Goldstein, Garry. Generalised route to effective field theories for quantum systems with local constraints. United States. https://doi.org/10.1103/PhysRevB.100.085113
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Szabo, Attila, Tsvelik, Alexei M., Castelnovo, Claudio, and Goldstein, Garry. Mon . "Generalised route to effective field theories for quantum systems with local constraints". United States. https://doi.org/10.1103/PhysRevB.100.085113. https://www.osti.gov/servlets/purl/1530523.
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@article{osti_1530523,
title = {Generalised route to effective field theories for quantum systems with local constraints},
author = {Szabo, Attila and Tsvelik, Alexei M. and Castelnovo, Claudio and Goldstein, Garry},
abstractNote = {Some of the exciting phenomena uncovered in strongly correlated systems in recent years – for instance quantum topological order, deconfined quantum criticality and emergent gauge symmetries – appear in systems where the Hilbert space is effectively projected at low energies in a way that imposes local constraints on the original degrees of freedom. Cases in point include spin liquids, valence bond systems, dimer and vertex models. In this work, we use a slave boson description coupled to a large-S path integral formulation to devise a generalised route to obtain effective field theories for such systems. We demonstrate the validity and capability of our approach by studying quantum dimer models and by comparing our results with the existing literature.Field theoretic approaches to date are limited to bipartite lattices, they depend on a gauge-symmetric under-standing of the constraint, and lack generic quantitative predictive power for the coefficients of the terms that appear in the Lagrangians of these systems. Our method overcomes all these shortcomings and we show how the results up to quadratic order compare with the known height description of the square lattice quantum dimer model, as well as with the numerical estimate of the speed of light of the photon excitations on the diamond lattice. Lastly, instanton considerations allow us to infer properties of the finite temperature behaviour in two dimensions.},
doi = {10.1103/PhysRevB.100.085113},
journal = {Physical Review B},
number = 8,
volume = 100,
place = {United States},
year = {Mon Jul 01 00:00:00 EDT 2019},
month = {Mon Jul 01 00:00:00 EDT 2019}
}
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Journal Article:
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https://doi.org/10.1103/PhysRevB.100.085113
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Figures / Tables:

FIG. 1 FIG. 1: Square lattice showing the choice of basis vectors e1,2.
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Works referenced in this record:

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Two classes of Mott insulator
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Compact gauge fields and the infrared catastrophe
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Pyrochlore photons: The U ( 1 ) spin liquid in a S = 1 2 three-dimensional frustrated magnet
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Bipartite Rokhsar–Kivelson points and Cantor deconfinement
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Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model
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Semiclassical approach to quantum spin ice
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Three-dimensional resonating-valence-bond liquids and their excitations
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d -wave superconductivity in boson+fermion dimer models
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Phase diagram of the hexagonal lattice quantum dimer model
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Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps
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Solving the quantum dimer and six-vertex models one electric field line at a time
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Properties of resonating-valence-bond spin liquids and critical dimer models
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Quantum Ice: A Quantum Monte Carlo Study
journal, February 2012

The “Coulomb Phase” in Frustrated Systems
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Extended quantum U ( 1 ) -liquid phase in a three-dimensional quantum dimer model
journal, September 2011

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model
text, January 2001

Finite-Volume Energy Spectrum, Fractionalized Strings, and Low-Energy Effective Field Theory for the Quantum Dimer Model on the Square Lattice
text, January 2016

  • Banerjee, D.; Bögli, M.; Hofmann, C. P.
  • Deutsches Elektronen-Synchrotron, DESY, Hamburg
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Phases of quantum dimers from ensembles of classical stochastic trajectories
text, January 2018

  • Oakes, T.; Powell, S.; Castelnovo, Claudio
  • Apollo - University of Cambridge Repository
  • DOI: 10.17863/cam.23369

Interfaces, strings, and a soft mode in the square lattice quantum dimer model
text, January 2014

  • Banerjee, Debasish; Widmer, Philippe; Wiese, Uwe-Jens
  • American Physical Society
  • DOI: 10.7892/boris.61520

D-wave superconductivity in boson+fermion dimer models
text, January 2017

  • Goldstein, Garry; Chamon, C.; Castelnovo, Claudio
  • Apollo - University of Cambridge Repository
  • DOI: 10.17863/cam.30179

Semiclassical approach to quantum spin ice
text, January 2017

  • Kwasigroch, Mp; Douçot, B.; Castelnovo, Claudio
  • Apollo - University of Cambridge Repository
  • DOI: 10.17863/cam.30821

Generic mixed columnar-plaquette phases in Rokhsar-Kivelson models
text, January 2007

Extended quantum U(1)-liquid phase in a three-dimensional quantum dimer model
text, January 2011

Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps
text, January 2015

Phases of quantum dimers from ensembles of classical stochastic trajectories
text, January 2018

Solving the quantum dimer and six vertex models one electric field line at a time
text, January 2019

The phase diagram of the hexagonal lattice quantum dimer model
text, January 2001

On bipartite Rokhsar-Kivelson points and Cantor deconfinement
text, January 2003

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    Figures / Tables found in this record:

    FIG. 1 (p. 4)figure
    FIG. 2 (p. 6)figure
    FIG. 3 (p. 8)figure
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    FIG. 5 (p. 11)figure
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    FIG. 8 (p. 12)figure
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    FIG. 11 (p. 14)figure
    FIG. 12 (p. 14)figure
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