Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

TRANSPORT PROPERTIES OF ANYONS

Dmitri V. Khveshchenko

Published Sep 10, 1992• 0 citations
Publisher

Abstract

We consider electromagnetic response as well as electrical and thermal transport in a normal state of anyon system at finite temperatures. We find the frequency and momentum dependences of electrical and thermal conductivities in the longwavelength limit. It is also shown that a pole of electric current and stress tensor correlation functions identified at zero temperature with a gapless sound-like mode becomes a diffusion above the critical temperature of the hypothetical superfluid anyon phase transition.

DOI
10.1142/s0217979292002267

Related papers

Critical scaling of thermal transport in model A dynamics for a superconductor

Iddo Ussishkin, David A. Huse, Shivaji L. Sondhi

We consider the scaling of thermal transport in the presence of electric and magnetic fields near the finite temperature transition from the metallic normal state to the superconductor. We do so with fully relaxational, model A, dynamics for the order parameter and particle-hole symmetry. This enables us to determine the exact scaling dimension of the heat current operator and hence critical exponents for all transport coefficients in terms of the (approximately) known values of the correlation length exponent and the dynamic scaling exponent. In particular, we determine the critical behavior for the Nernst coefficient.

arXiv:cond-mat/0411040•Nov 2, 2004•1 citation

Transport and conservation laws

X. Zotos, Félix Naef, Peter Prelovšek

We study the effect of conservation laws on the finite-temperature transport properties in one-dimensional integrable quantum many-body systems. We show that the energy current is closely related to the first conservation law in these systems and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero-frequency component of the conductivity) and so ideal conductivity at finite temperatures.

arXiv:cond-mat/9611007•Physical review. B, Condensed matter•May 1, 1997•533 citations

Heat transport in the anisotropic Kitaev spin liquid

Angelo Pidatella, Alexandros Metavitsiadis, Wolfram Brenig

We present a study of longitudinal thermal transport in the Kitaev spin model on the honeycomb lattice, focusing on the role of anisotropic exchange to cover both gapless and gapped phases. Employing a complementary combination of exact diagonalization on small systems and an average gauge configuration approach for up to $\ensuremath{\sim}O({10}^{4})$ spinful sites, we report results for the dynamical energy current autocorrelation function as well as the dc thermal conductivity over a wide range of temperatures and exchange anisotropies. Despite a pseudogap in the current correlation spectra, induced by emergent thermal gauge disorder on any finite system, we find that in the thermodynamic limit, gapless and gapful phases both feature normal dissipative transport, with a temperature dependence crossing over from power law to exponentially activated behavior upon gap opening.

arXiv:1810.04674•Physical review. B./Physical review. B•Feb 20, 2019•19 citations

Transport in a one-dimensional hyperconductor

Eugeniu Plamadeala, Michael Mulligan, Chetan Nayak

We define a ``hyperconductor'' to be a material whose electrical and thermal dc conductivities are infinite at zero temperature and finite at any nonzero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially gap-generating interactions and potentially localizing disorder. In this paper, we compute the low-temperature dc and ac electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, which allows us to exhibit examples of violations of the Wiedemann-Franz law. The temperature dependence of the electrical conductivity, which is characterized by the parameter ${\mathrm{\ensuremath{\Delta}}}_{X}$, is a power law, $\ensuremath{\sigma}\ensuremath{\propto}1/{T}^{1\ensuremath{-}2(2\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{X})}$ when ${\mathrm{\ensuremath{\Delta}}}_{X}\ensuremath{\ge}2$, down to zero temperature when the Fermi surface is commensurate with the lattice. There is a surface in parameter space along which ${\mathrm{\ensuremath{\Delta}}}_{X}=2$ and ${\mathrm{\ensuremath{\Delta}}}_{X}\ensuremath{\approx}2$ for small deviations from this surface. In the generic (incommensurate) case with weak disorder, such scaling is seen at high temperatures, followed by an exponential increase of the conductivity $ln\ensuremath{\sigma}\ensuremath{\sim}1/T$ at intermediate temperatures and, finally, $\ensuremath{\sigma}\ensuremath{\propto}1/{T}^{2\ensuremath{-}2(2\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{X})}$ at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.

arXiv:1509.04280•Physical review. B./Physical review. B•Mar 29, 2016•3 citations

THERMAL PROPERTIES AND GROUND STATE ENERGY SHIFT OF CHARGED ANYONS

J.Y. Kim, Yun Soo Myung, S.H. Yi

We derive the second and third virial coefficients and the ground state energy shift for charged anyons within the Hartree-Fock approximation. A second quantization scheme at finite temperature is introduced for this calculation up to the second order and the vertex is composed of anyonic, point, constant as well as Coulomb interactions. The thermodynamic potential for the second order correlation diagram of Coulomb interaction leads to the logarithmic divergence (V ln V). Hence, we find the heat capacity and the correlation energy of anyons without Coulomb-Coulomb interaction. Finally, we discuss the magnetic-field-induced localization at low filling ν, including the Wigner crystal phase.

International Journal of Modern Physics A•Aug 10, 1994•0 citations

Dynamique et transport au voisinage d'une transition de phase quantique en dimension deux

Félix Rose

We study the relativistic O (N) model, a quantum generalization of the φ⁴ theory used in statistical physics to study some phase transitions. This model describes quantum phase transitions such as the Mott insulator-superluid transition in boson gases trapped in optical latices or the paramagnetic-antiferromagnetic transition in magnets. In two space dimensions, these systems exhibit strong correlations near the transition. We study them using the nonperturbative renormalization group, an implementation of Wilson’s renormalization group. We focus on the universal properties in the vicinity of the zero-temperature quantum phase transition. We determine the universal scaling functions which define the thermodynamics and we show that these functions are related to those describing the critical Casimir forces in a three-dimensional system. Then, we study the excitation spectrum in the zero-temperature ordered phase. For N = 2 and 3, we establish the existence of an amplitude mode, also called “Higgs mode” by analogy with the Higgs mechanism in high-energy physics. For N = 1, we show the existence of a bound state at dimensions close to three. Finally, we compute the frequency-dependent conductivity at zero temperature and confirm its universal character, in particular at the transition. We prove that one of the components of the conductivity tensor in the ordered phase is a “superuniversal” quantity depending neither on the distance to the critical point nor on N.

•Sep 19, 2017•0 citations
We consider electromagnetic response as well as electrical and thermal transport in a normal state of anyon system at finite temperatures. We find the frequency and momentum dependences of electrical and thermal conductivities in the longwavelength limit. It is also shown that a pole of electric current and stress tensor correlation functions identified at zero temperature with a gapless sound-like mode becomes a diffusion above the critical temperature of the hypothetical superfluid anyon phase transition.
We consider the scaling of thermal transport in the presence of electric and magnetic fields near the finite temperature transition from the metallic normal state to the superconductor. We do so with fully relaxational, model A, dynamics for the order parameter and particle-hole symmetry. This enables us to determine the exact scaling dimension of the heat current operator and hence critical exponents for all transport coefficients in terms of the (approximately) known values of the correlation length exponent and the dynamic scaling exponent. In particular, we determine the critical behavior for the Nernst coefficient.
We study the effect of conservation laws on the finite-temperature transport properties in one-dimensional integrable quantum many-body systems. We show that the energy current is closely related to the first conservation law in these systems and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero-frequency component of the conductivity) and so ideal conductivity at finite temperatures.
We present a study of longitudinal thermal transport in the Kitaev spin model on the honeycomb lattice, focusing on the role of anisotropic exchange to cover both gapless and gapped phases. Employing a complementary combination of exact diagonalization on small systems and an average gauge configuration approach for up to $\ensuremath{\sim}O({10}^{4})$ spinful sites, we report results for the dynamical energy current autocorrelation function as well as the dc thermal conductivity over a wide range of temperatures and exchange anisotropies. Despite a pseudogap in the current correlation spectra, induced by emergent thermal gauge disorder on any finite system, we find that in the thermodynamic limit, gapless and gapful phases both feature normal dissipative transport, with a temperature dependence crossing over from power law to exponentially activated behavior upon gap opening.
We define a ``hyperconductor'' to be a material whose electrical and thermal dc conductivities are infinite at zero temperature and finite at any nonzero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially gap-generating interactions and potentially localizing disorder. In this paper, we compute the low-temperature dc and ac electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, which allows us to exhibit examples of violations of the Wiedemann-Franz law. The temperature dependence of the electrical conductivity, which is characterized by the parameter ${\mathrm{\ensuremath{\Delta}}}_{X}$, is a power law, $\ensuremath{\sigma}\ensuremath{\propto}1/{T}^{1\ensuremath{-}2(2\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{X})}$ when ${\mathrm{\ensuremath{\Delta}}}_{X}\ensuremath{\ge}2$, down to zero temperature when the Fermi surface is commensurate with the lattice. There is a surface in parameter space along which ${\mathrm{\ensuremath{\Delta}}}_{X}=2$ and ${\mathrm{\ensuremath{\Delta}}}_{X}\ensuremath{\approx}2$ for small deviations from this surface. In the generic (incommensurate) case with weak disorder, such scaling is seen at high temperatures, followed by an exponential increase of the conductivity $ln\ensuremath{\sigma}\ensuremath{\sim}1/T$ at intermediate temperatures and, finally, $\ensuremath{\sigma}\ensuremath{\propto}1/{T}^{2\ensuremath{-}2(2\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{X})}$ at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.
We derive the second and third virial coefficients and the ground state energy shift for charged anyons within the Hartree-Fock approximation. A second quantization scheme at finite temperature is introduced for this calculation up to the second order and the vertex is composed of anyonic, point, constant as well as Coulomb interactions. The thermodynamic potential for the second order correlation diagram of Coulomb interaction leads to the logarithmic divergence (V ln V). Hence, we find the heat capacity and the correlation energy of anyons without Coulomb-Coulomb interaction. Finally, we discuss the magnetic-field-induced localization at low filling ν, including the Wigner crystal phase.
We study the relativistic O (N) model, a quantum generalization of the φ⁴ theory used in statistical physics to study some phase transitions. This model describes quantum phase transitions such as the Mott insulator-superluid transition in boson gases trapped in optical latices or the paramagnetic-antiferromagnetic transition in magnets. In two space dimensions, these systems exhibit strong correlations near the transition. We study them using the nonperturbative renormalization group, an implementation of Wilson’s renormalization group. We focus on the universal properties in the vicinity of the zero-temperature quantum phase transition. We determine the universal scaling functions which define the thermodynamics and we show that these functions are related to those describing the critical Casimir forces in a three-dimensional system. Then, we study the excitation spectrum in the zero-temperature ordered phase. For N = 2 and 3, we establish the existence of an amplitude mode, also called “Higgs mode” by analogy with the Higgs mechanism in high-energy physics. For N = 1, we show the existence of a bound state at dimensions close to three. Finally, we compute the frequency-dependent conductivity at zero temperature and confirm its universal character, in particular at the transition. We prove that one of the components of the conductivity tensor in the ordered phase is a “superuniversal” quantity depending neither on the distance to the critical point nor on N.