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Title: Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods appliedmore » to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less
Authors:
ORCiD logo [1] ; ORCiD logo [2] ;  [3] ; ORCiD logo [2] ;  [2]
  1. Univ. College, London (United Kingdom). London Centre for Nanotechnology
  2. Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.
  3. Univ. de Cergy-Pontoise, Cergy-Pontoise Cedex (France). Lab. de Physique Theorique et Modelisation
Publication Date:
Report Number(s):
BNL-203532-2018-JAAM
Journal ID: ISSN 0034-4885; TRN: US1802549
Grant/Contract Number:
SC0012704
Type:
Accepted Manuscript
Journal Name:
Reports on Progress in Physics
Additional Journal Information:
Journal Volume: 81; Journal Issue: 4; Journal ID: ISSN 0034-4885
Publisher:
IOP Publishing
Research Org:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; low dimensional correlated systems; non-Abelian bosonization; truncated conformal space approach; numerical renormalization group; matrix product states; integrability; non-equilibrium dynamics
OSTI Identifier:
1433990

James, Andrew J. A., Konik, Robert M., Lecheminant, Philippe, Robinson, Neil J., and Tsvelik, Alexei M.. Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods. United States: N. p., Web. doi:10.1088/1361-6633/aa91ea.
James, Andrew J. A., Konik, Robert M., Lecheminant, Philippe, Robinson, Neil J., & Tsvelik, Alexei M.. Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods. United States. doi:10.1088/1361-6633/aa91ea.
James, Andrew J. A., Konik, Robert M., Lecheminant, Philippe, Robinson, Neil J., and Tsvelik, Alexei M.. 2018. "Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods". United States. doi:10.1088/1361-6633/aa91ea.
@article{osti_1433990,
title = {Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods},
author = {James, Andrew J. A. and Konik, Robert M. and Lecheminant, Philippe and Robinson, Neil J. and Tsvelik, Alexei M.},
abstractNote = {We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.},
doi = {10.1088/1361-6633/aa91ea},
journal = {Reports on Progress in Physics},
number = 4,
volume = 81,
place = {United States},
year = {2018},
month = {2}
}