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

arXiv:0903.0590 · International Journal of Modern Physics B

DECONFINEMENT AND QUANTUM LIQUID CRYSTALLINE STATES OF DIPOLAR FERMIONS IN OPTICAL LATTICES

SAM T. CARR, Jorge Quintanilla, JOSEPH J. BETOURAS

Published Aug 20, 2009• 5 citations
arXivHTMLPDF

Abstract

We describe a simple model of fermions in quasi-one dimension that features interaction-induced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice1. The model provides a relisation of a "soft quantum matter" phase diagram of strongly-correlated fermions, featuring meta-nematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on the basis of bosonization and detailed analysis of the RPA susceptibility.

DOI
10.1142/s0217979209063262

Related papers

Metanematic, smectic, and crystalline phases of dipolar fermions in an optical lattice

Jorge Quintanilla, Sam T. Carr, Joseph J. Betouras

It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realization of this soft quantum matter physics in an ultracold gas. It uses optical lattices and dipolar interactions to realize a particularly simple model. Our analysis reveals a rich phase diagram featuring a metanematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes) and a crystalline ``checkerboard'' phase.

arXiv:0803.2708•Physical Review A•Mar 26, 2009•49 citations

Liquid crystal phases of ultracold dipolar fermions on a lattice

Chungwei Lin, Erhai Zhao, W. Vincent Liu

Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density-wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x\text{\ensuremath{-}}y$ plane) with dipoles pointing to the $z$ direction. We determine the phase diagram using two complementary methods, the Hartree-Fock mean-field theory and the linear-response analysis of compressibility. Both give consistent results. In addition to the staggered $(\ensuremath{\pi},\ensuremath{\pi})$ density wave, over a finite range of densities and hopping parameters, the ground state of the system first becomes nematic and then smectic, when the dipolar interaction strength is increased. Both phases are characterized by the same broken fourfold $({C}_{4})$ rotational symmetry. The difference is that the nematic phase has a closed Fermi surface but the smectic does not. The transition from the nematic to the smectic phase is associated with a jump in the nematic order parameter. This jump is closely related to the Van Hove singularities. We derive the kinetic equation for collective excitations in the normal isotropic phase and find that the zero sound mode is strongly Landau damped and thus is not a well-defined excitation. Experimental implications of our results are discussed.

arXiv:0909.5267•Physical Review B•Jan 13, 2010•39 citations

DECONFINEMENT AND COLD ATOMS IN OPTICAL LATTICES

M. A CAZALILLA, A. F. HO, Thierry Giamarchi

Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.

arXiv:cond-mat/0604525•International Journal of Modern Physics B•Dec 15, 2006•0 citations

Dipolar interaction driven phase transitions in a one-dimensional optical lattice with a synthetic dimension

Yu-Hang Li, Hua Chen, Xiaoming Xie

Extensive research interest has been attracted by the fact that recent experiments in cold atoms simulate the chiral edge states of (1 + 1)-dimensional quantum Hall systems with laser-assisted transitions between different atomic nuclear spin states in a one-dimensional optical lattice. Within such an optical lattice, we study the phase diagrams of ν = 1 / 3 filling hard-core fermions and ν = 1 / 2 hard-core bosons with internal spin states in the presence of dipole-dipolar interactions. Our results show that the interaction drives the fermionic (bosonic) systems from the normal (superfluid) phase into the fractional topological phase with possible crystalline orderings. The topological nature of the latter phase is identified by the numerical evaluation of the many-body Chern number. Remarkably, we find that a considerable spectrum gap stabilizes the fractional topological phase with a moderate interaction strength, while, for the normal/superfluid phase, the Thouless charge pumping fluctuates strongly for small spin systems but approaches its universal value 1/3 for fermionic and 1/2 for bosonic systems with large spins.

Europhysics Letters (EPL)•Feb 1, 2017•2 citations

Strongly correlated bosons and fermions in optical lattices

Antoine Georges, Thierry Giamarchi

This chapter gives an introduction to the physics of interacting quantum systems, both bosonic and fermionic. Section 1.2 introduces the physics of quantum particles in periodic lattices. Section 1.3 examines, for the case of bosons, how the combined effects of lattice and interaction can turn the system into an insulator, the so-called Mott insulator, and discusses the corresponding physics. Section 1.4 discusses what happens when the system is one-dimensional. Section 1.5 moves on to the case of fermions. It discusses first Fermi-liquid theory and the concept of quasi-particles, Landau’s description of the low-energy excitations of interacting fermion systems. Section 1.6 shows how, like the method for bosons, the combination of a lattice and strong interactions can turn a Fermi liquid into a Mott insulator. Section 1.7 looks at the properties of one-dimensional fermions, shows how Fermi liquid theory fails because low-energy excitations are now collective modes instead of quasi-particles, and examines the corresponding physics for both the conducting and insulating phases. Finally, Section 1.8 draws some conclusions and give some perspectives.

Oxford University Press eBooks•Nov 15, 2012•33 citations

Bose-Fermi solid and its quantum melting in a one-dimensional optical lattice

Bin Wang, Daw-Wei Wang, S. Das Sarma

We investigate the quantum phase diagram of Bose-Fermi mixtures of ultracold dipolar particles trapped in one-dimensional optical lattices in the thermodynamic limit. With the presence of nearest-neighbor (NN) interactions, a long-ranged ordered crystalline phase (Bose-Fermi solid) is found stabilized in the limit of weak intersite tunneling ($J$). When $J$ is increased, such a Bose-Fermi solid can be quantum melted into a Bose-Fermi liquid through different procedures, depending on whether the crystalline order is dominated by the NN interaction between fermions or bosons. These properties are qualitatively different from the classical picture of solid-liquid phase transition.

arXiv:1004.5129•Physical Review A•Aug 10, 2010•8 citations
We describe a simple model of fermions in quasi-one dimension that features interaction-induced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice1. The model provides a relisation of a "soft quantum matter" phase diagram of strongly-correlated fermions, featuring meta-nematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on the basis of bosonization and detailed analysis of the RPA susceptibility.
It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realization of this soft quantum matter physics in an ultracold gas. It uses optical lattices and dipolar interactions to realize a particularly simple model. Our analysis reveals a rich phase diagram featuring a metanematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes) and a crystalline ``checkerboard'' phase.
Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density-wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x\text{\ensuremath{-}}y$ plane) with dipoles pointing to the zzz direction. We determine the phase diagram using two complementary methods, the Hartree-Fock mean-field theory and the linear-response analysis of compressibility. Both give consistent results. In addition to the staggered $(\ensuremath{\pi},\ensuremath{\pi})$ density wave, over a finite range of densities and hopping parameters, the ground state of the system first becomes nematic and then smectic, when the dipolar interaction strength is increased. Both phases are characterized by the same broken fourfold (C4)({C}_{4})(C4​) rotational symmetry. The difference is that the nematic phase has a closed Fermi surface but the smectic does not. The transition from the nematic to the smectic phase is associated with a jump in the nematic order parameter. This jump is closely related to the Van Hove singularities. We derive the kinetic equation for collective excitations in the normal isotropic phase and find that the zero sound mode is strongly Landau damped and thus is not a well-defined excitation. Experimental implications of our results are discussed.
Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.
Extensive research interest has been attracted by the fact that recent experiments in cold atoms simulate the chiral edge states of (1 + 1)-dimensional quantum Hall systems with laser-assisted transitions between different atomic nuclear spin states in a one-dimensional optical lattice. Within such an optical lattice, we study the phase diagrams of ν = 1 / 3 filling hard-core fermions and ν = 1 / 2 hard-core bosons with internal spin states in the presence of dipole-dipolar interactions. Our results show that the interaction drives the fermionic (bosonic) systems from the normal (superfluid) phase into the fractional topological phase with possible crystalline orderings. The topological nature of the latter phase is identified by the numerical evaluation of the many-body Chern number. Remarkably, we find that a considerable spectrum gap stabilizes the fractional topological phase with a moderate interaction strength, while, for the normal/superfluid phase, the Thouless charge pumping fluctuates strongly for small spin systems but approaches its universal value 1/3 for fermionic and 1/2 for bosonic systems with large spins.
This chapter gives an introduction to the physics of interacting quantum systems, both bosonic and fermionic. Section 1.2 introduces the physics of quantum particles in periodic lattices. Section 1.3 examines, for the case of bosons, how the combined effects of lattice and interaction can turn the system into an insulator, the so-called Mott insulator, and discusses the corresponding physics. Section 1.4 discusses what happens when the system is one-dimensional. Section 1.5 moves on to the case of fermions. It discusses first Fermi-liquid theory and the concept of quasi-particles, Landau’s description of the low-energy excitations of interacting fermion systems. Section 1.6 shows how, like the method for bosons, the combination of a lattice and strong interactions can turn a Fermi liquid into a Mott insulator. Section 1.7 looks at the properties of one-dimensional fermions, shows how Fermi liquid theory fails because low-energy excitations are now collective modes instead of quasi-particles, and examines the corresponding physics for both the conducting and insulating phases. Finally, Section 1.8 draws some conclusions and give some perspectives.
We investigate the quantum phase diagram of Bose-Fermi mixtures of ultracold dipolar particles trapped in one-dimensional optical lattices in the thermodynamic limit. With the presence of nearest-neighbor (NN) interactions, a long-ranged ordered crystalline phase (Bose-Fermi solid) is found stabilized in the limit of weak intersite tunneling (JJJ). When JJJ is increased, such a Bose-Fermi solid can be quantum melted into a Bose-Fermi liquid through different procedures, depending on whether the crystalline order is dominated by the NN interaction between fermions or bosons. These properties are qualitatively different from the classical picture of solid-liquid phase transition.