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:cond-mat/9807204 · Physical review. B, Condensed matter

Collapse of the charge gap in random Mott insulators

Yuichi Otsuka, Yoshifumi Morita, Yasuhiro Hatsugai

Published Dec 15, 1998• 19 citations
arXivHTMLPDF

Abstract

Effects of randomness on interacting fermionic systems in one dimension are investigated by quantum Monte Carlo techniques. At first, interacting spinless fermions are studied whose ground state shows charge ordering. Quantum phase transition due to randomness is observed associated with the collapse of the charge ordering. We also treat random Hubbard model focusing on the Mott gap. Although the randomness closes the Mott gap and low-lying states are created, which is observed in the charge compressibility, no (quasi-)Fermi-surface singularity is formed. It implies localized nature of the low-lying states.

DOI
10.1103/physrevb.58.15314

Related papers

Numerical study of the effects of disorder on the three-dimensional Hubbard model

Yuichi Otsuka, Yasuhiro Hatsugai

The combined effects of interactions and disorder are investigated using a finite-temperature quantum Monte Carlo technique for the three-dimensional Hubbard model with random potentials of finite range. The temperature dependence of the charge compressibility shows that the Mott gap seems to collapse beyond a finite disorder strength. This is a quantum phase transition from an incompressible phase to a compressible phase driven by disorder. We calculate the antiferromagnetic structure factor in the presence of disorder as well. Strong antiferromagnetic correlation, which is characteristic of the Mott insulator, is destroyed by the presence of a finite amount of disorder.

arXiv:cond-mat/0005270•Journal of Physics Condensed Matter•Oct 18, 2000•20 citations

Effect of randomness on the Mott state

Hanbin Pang, Shoudan Liang, James F. Annett

Competition between Mott and Anderson metal-insulator transitions is studied in a one dimensional spinless fermion system of 200 sites. Although the long range charge density wave (CDW) order and gap of the Mott phase are destroyed by weak randomness, the elementary excitations are still solitons based on the local CDW order. The solitons are easily localized in the random potential. Thus for weak randomness and large interaction, a disordered Mott phase exists in which the localization is determined by the local CDW order in contrast to the conventional Anderson localization picture in the weak interaction limit.

Physical Review Letters•Dec 27, 1993•26 citations

Gap-opening transition and fractal ground-state phase diagram in one-dimensional fermions with long-range interaction: Mott transition as a quantum phase transition of infinite order

Yasuhiro Hatsugai

The metal-insulator transition in one-dimensional fermionic systems with long-range interaction is investigated. We have focused on an excitation spectrum by the exact diagonalization technique in sectors with different momentum quantum numbers. At rational fillings, we have demonstrated gap opening transitions from the Tomonaga-Luttinger liquid to the Mott insulator associated with a discrete symmetry breaking by changing the interaction strength. Finite interaction range is crucial to have the Mott transition at a rational filling away from the half filling. It is consistent with the strong coupling picture where the Mott gap exists at any rational fillings with sufficiently strong interaction. The critical regions as a quantum phase transition are also investigated numerically. Nonanalytic behavior of the Mott gap is the characteristic in the weak coupling. It is of the order of the interaction in the strong coupling. It implies that the metal-insulator transition of the model is of the infinite order as a quantum phase transition at zero temperature. The fractal nature of the ground-state phase diagram is also revealed.

arXiv:cond-mat/9701158•Physical review. B, Condensed matter•Nov 15, 1997•13 citations

Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices

Marcos Rigol, Alejandro Muramatsu

Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulating transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.

arXiv:cond-mat/0309670•Physical Review A•May 14, 2004•85 citations

Quantum phase transitions and collapse of the Mott gap in the d=1+ε dimensional Hubbard model with 2kF umklapp scattering

Jun‐ichiro Kishine

We study the low-energy asymptotics of the $d=1+\ensuremath{\epsilon}$ dimensional Hubbard model with a circular Fermi surface where there is ${2k}_{F}$ umklapp scattering present a priori. Peculiarity of the $d=1+\ensuremath{\epsilon}$ dimensions is incorporated through the imbalance between the elementary particle-particle and particle-hole (PH) loops: infrared logarithmic singularity of the PH loop is smeared for $\ensuremath{\epsilon}>0.$ The one-loop renormalization-group flows indicate that a quantum phase transition from a metallic phase to the Mott insulator phase occurs at a finite on-site Coulomb repulsion U for $\ensuremath{\epsilon}>0.$ We also discuss effects of randomness.

arXiv:cond-mat/9910471•Physical review. B, Condensed matter•Jul 15, 2000•4 citations

Local Mott metal-insulator transition in confined fermions on optical lattices

Marcos Rigol

Using quantum Monte Carlo (QMC) simulations we study the ground state properties of the one‐dimensional fermionic Hubbard model in traps with an underlying lattice. We show that this model displays quantum critical behavior at the boundaries of the local Mott‐insulating regions. A local compressibility defined to characterize the Mott‐insulating phase has a non‐trivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We study the momentum distribution function and we find that it is not appropriate to characterize the transitions in the system.

AIP conference proceedings•Jan 1, 2004•0 citations
Effects of randomness on interacting fermionic systems in one dimension are investigated by quantum Monte Carlo techniques. At first, interacting spinless fermions are studied whose ground state shows charge ordering. Quantum phase transition due to randomness is observed associated with the collapse of the charge ordering. We also treat random Hubbard model focusing on the Mott gap. Although the randomness closes the Mott gap and low-lying states are created, which is observed in the charge compressibility, no (quasi-)Fermi-surface singularity is formed. It implies localized nature of the low-lying states.
The combined effects of interactions and disorder are investigated using a finite-temperature quantum Monte Carlo technique for the three-dimensional Hubbard model with random potentials of finite range. The temperature dependence of the charge compressibility shows that the Mott gap seems to collapse beyond a finite disorder strength. This is a quantum phase transition from an incompressible phase to a compressible phase driven by disorder. We calculate the antiferromagnetic structure factor in the presence of disorder as well. Strong antiferromagnetic correlation, which is characteristic of the Mott insulator, is destroyed by the presence of a finite amount of disorder.
Competition between Mott and Anderson metal-insulator transitions is studied in a one dimensional spinless fermion system of 200 sites. Although the long range charge density wave (CDW) order and gap of the Mott phase are destroyed by weak randomness, the elementary excitations are still solitons based on the local CDW order. The solitons are easily localized in the random potential. Thus for weak randomness and large interaction, a disordered Mott phase exists in which the localization is determined by the local CDW order in contrast to the conventional Anderson localization picture in the weak interaction limit.
The metal-insulator transition in one-dimensional fermionic systems with long-range interaction is investigated. We have focused on an excitation spectrum by the exact diagonalization technique in sectors with different momentum quantum numbers. At rational fillings, we have demonstrated gap opening transitions from the Tomonaga-Luttinger liquid to the Mott insulator associated with a discrete symmetry breaking by changing the interaction strength. Finite interaction range is crucial to have the Mott transition at a rational filling away from the half filling. It is consistent with the strong coupling picture where the Mott gap exists at any rational fillings with sufficiently strong interaction. The critical regions as a quantum phase transition are also investigated numerically. Nonanalytic behavior of the Mott gap is the characteristic in the weak coupling. It is of the order of the interaction in the strong coupling. It implies that the metal-insulator transition of the model is of the infinite order as a quantum phase transition at zero temperature. The fractal nature of the ground-state phase diagram is also revealed.
Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulating transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.
We study the low-energy asymptotics of the $d=1+\ensuremath{\epsilon}$ dimensional Hubbard model with a circular Fermi surface where there is 2kF{2k}_{F}2kF​ umklapp scattering present a priori. Peculiarity of the $d=1+\ensuremath{\epsilon}$ dimensions is incorporated through the imbalance between the elementary particle-particle and particle-hole (PH) loops: infrared logarithmic singularity of the PH loop is smeared for $\ensuremath{\epsilon}>0.$ The one-loop renormalization-group flows indicate that a quantum phase transition from a metallic phase to the Mott insulator phase occurs at a finite on-site Coulomb repulsion U for $\ensuremath{\epsilon}>0.$ We also discuss effects of randomness.
Using quantum Monte Carlo (QMC) simulations we study the ground state properties of the one‐dimensional fermionic Hubbard model in traps with an underlying lattice. We show that this model displays quantum critical behavior at the boundaries of the local Mott‐insulating regions. A local compressibility defined to characterize the Mott‐insulating phase has a non‐trivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We study the momentum distribution function and we find that it is not appropriate to characterize the transitions in the system.