Nonperturbative methodologies for lowdimensional stronglycorrelated systems: From nonAbelian bosonization to truncated spectrum methods
Abstract
We review two important nonperturbative approaches for extracting the physics of lowdimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of nonAbelian 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 nonAbelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For onedimensional 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 sineGordon 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 onedimensional systems: properties of carbon nanotubes, quenches in the LiebLiniger model, 1+1D quantum chromodynamics, as well as LandauGinzburg theories. In the final part we move our attention to consider truncated spectrum methods appliedmore »
 Authors:

 Univ. College, London (United Kingdom). London Centre for Nanotechnology
 Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.
 Univ. de CergyPontoise, CergyPontoise Cedex (France). Lab. de Physique Theorique et Modelisation
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1433990
 Report Number(s):
 BNL2035322018JAAM
Journal ID: ISSN 00344885; TRN: US1802549
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Reports on Progress in Physics
 Additional Journal Information:
 Journal Volume: 81; Journal Issue: 4; Journal ID: ISSN 00344885
 Publisher:
 IOP Publishing
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; low dimensional correlated systems; nonAbelian bosonization; truncated conformal space approach; numerical renormalization group; matrix product states; integrability; nonequilibrium dynamics
Citation Formats
James, Andrew J. A., Konik, Robert M., Lecheminant, Philippe, Robinson, Neil J., and Tsvelik, Alexei M. Nonperturbative methodologies for lowdimensional stronglycorrelated systems: From nonAbelian bosonization to truncated spectrum methods. United States: N. p., 2018.
Web. doi:10.1088/13616633/aa91ea.
James, Andrew J. A., Konik, Robert M., Lecheminant, Philippe, Robinson, Neil J., & Tsvelik, Alexei M. Nonperturbative methodologies for lowdimensional stronglycorrelated systems: From nonAbelian bosonization to truncated spectrum methods. United States. doi:10.1088/13616633/aa91ea.
James, Andrew J. A., Konik, Robert M., Lecheminant, Philippe, Robinson, Neil J., and Tsvelik, Alexei M. Mon .
"Nonperturbative methodologies for lowdimensional stronglycorrelated systems: From nonAbelian bosonization to truncated spectrum methods". United States. doi:10.1088/13616633/aa91ea. https://www.osti.gov/servlets/purl/1433990.
@article{osti_1433990,
title = {Nonperturbative methodologies for lowdimensional stronglycorrelated systems: From nonAbelian 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 nonperturbative approaches for extracting the physics of lowdimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of nonAbelian 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 nonAbelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For onedimensional 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 sineGordon 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 onedimensional systems: properties of carbon nanotubes, quenches in the LiebLiniger model, 1+1D quantum chromodynamics, as well as LandauGinzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to twodimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to twodimensional systems of free fermions and the quantum Ising model, including their nonequilibrium dynamics.},
doi = {10.1088/13616633/aa91ea},
journal = {Reports on Progress in Physics},
number = 4,
volume = 81,
place = {United States},
year = {2018},
month = {2}
}
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