In this paper we study the properties of a gas of fermions coupling to a U(1) gauge field at wave vectors $q<\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ at dimensions larger than 1, where $\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ is a high-momentum cutoff and ${k}_{F}$ is the Fermi wave vector. In particular, we shall consider the ${e}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where charge and current fluctuations at wave vectors $q<\ensuremath{\Lambda}$ are forbidden. By generalizing a method reported in a previous paper [Phys. Rev. B 62, 7019 (2000)], we show that the system can be described as a ``marginal'' Fermi liquid of spin $1/2;$ chargeless fermions with vanishing wave functions overlap with the bare fermions in the system.In this paper we study the properties of a gas of fermions coupling to a U(1) gauge field at wave vectors $q<\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ at dimensions larger than 1, where $\ensuremath{\Lambda}\ensuremath{\ll}{k}_{F}$ is a high-momentum cutoff and ${k}_{F}$ is the Fermi wave vector. In particular, we shall consider the ${e}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where charge and current fluctuations at wave vectors $q<\ensuremath{\Lambda}$ are forbidden. By generalizing a method reported in a previous paper [Phys. Rev. B 62, 7019 (2000)], we show that the system can be described as a ``marginal'' Fermi liquid of spin $1/2;$ chargeless fermions with vanishing wave functions overlap with the bare fermions in the system.

arXiv:cond-mat/0010306Physical review. B, Condensed matterJun 4, 20012 citations

Phase transitions of fermions coupled to a gauge field: a quantum Monte Carlo approach

Matthias H. Hettler, K. Ziegler

arXiv:cond-mat/9505078Physica A Statistical Mechanics and its ApplicationsSep 1, 19950 citations

Gauge theory of nonrelativistic fermions and its low-energy behavior

Ikuo Ichinose, Tetsuo Matsui

Nuclear Physics BMay 1, 199513 citations

Hybrid Quantum Monte Carlo Simulations of an Unconstrained U(1) Lattice Gauge Theory with Fermionic Matter

Ahlqvist Edwin

We study a compact U(1) lattice gauge theory using a self-built Hybrid Monte Carlo (HMC) program. The starting point is the parton construction of the Heisenberg spin chain where the spins are fractionalized into spinons coupled to an emergent compact U(1) gauge field. Here we do not impose Gauss's law, such that the Hamiltonian describes an unconstrained lattice gauge theory. We make theoretical calculations of the ground-state phase diagram and identify an emergent SO(4) symmetry in the strong-coupling limit. Furthermore, the weak coupling limit corresponds to frozen gauge fields which results in a free fermionic phase that is unstable in one dimension. The phase diagram is supported by carrying out HMC simulations which also allow us to study the dynamical generation of Gauss's law at low energy scales. We find that the theory accurately predicts the numerical findings and establish that HMC works as a method for simulating unconstrained gauge theories in (1+1)-dimensions.We study a compact U(1) lattice gauge theory using a self-built Hybrid Monte Carlo (HMC) program. The starting point is the parton construction of the Heisenberg spin chain where the spins are fractionalized into spinons coupled to an emergent compact U(1) gauge field. Here we do not impose Gauss's law, such that the Hamiltonian describes an unconstrained lattice gauge theory. We make theoretical calculations of the ground-state phase diagram and identify an emergent SO(4) symmetry in the strong-coupling limit. Furthermore, the weak coupling limit corresponds to frozen gauge fields which results in a free fermionic phase that is unstable in one dimension. The phase diagram is supported by carrying out HMC simulations which also allow us to study the dynamical generation of Gauss's law at low energy scales. We find that the theory accurately predicts the numerical findings and establish that HMC works as a method for simulating unconstrained gauge theories in (1+1)-dimensions.

Jan 1, 20260 citations

Fermions in interaction with time-dependent fields

P. Falkensteiner, Harald Grosse

Nuclear Physics BSep 1, 19888 citations

Deconfinement in the presence of a Fermi surface

Ki‐Seok Kim

U(1) gauge theory of nonrelativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions $({\mathrm{QED}}_{3})$ by [Hermele et al.Phys. Rev. B 70, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ [the coupling strength between nonrelativistic fermions and U(1) gauge fields] reveals that the conductivity $\ensuremath{\sigma}$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in ${\mathrm{QED}}_{3}$ . This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the nonrelativistic fermions at the charged fixed point. As a result a critical field theory of nonrelativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point.U(1) gauge theory of nonrelativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions $({\mathrm{QED}}_{3})$ by [Hermele et al.Phys. Rev. B 70, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ [the coupling strength between nonrelativistic fermions and U(1) gauge fields] reveals that the conductivity $\ensuremath{\sigma}$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in ${\mathrm{QED}}_{3}$. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the nonrelativistic fermions at the charged fixed point. As a result a critical field theory of nonrelativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point.

arXiv:cond-mat/0502652Physical Review BDec 7, 200518 citations

{k}_{F}

is the Fermi wave vector. In particular, we shall consider the ${e}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where charge and current fluctuations at wave vectors $q<\ensuremath{\Lambda}$ are forbidden. By generalizing a method reported in a previous paper [Phys. Rev. B 62, 7019 (2000)], we show that the system can be described as a ``marginal'' Fermi liquid of spin

1/2;

chargeless fermions with vanishing wave functions overlap with the bare fermions in the system.

({\mathrm{QED}}_{3})

by [Hermele et al.Phys. Rev. B 70, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge

e

[the coupling strength between nonrelativistic fermions and U(1) gauge fields] reveals that the conductivity $\ensuremath{\sigma}$ of fermions near the Fermi surface plays the same role as the flavor number

N

of massless Dirac fermions in

{\mathrm{QED}}_{3}

. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the nonrelativistic fermions at the charged fixed point. As a result a critical field theory of nonrelativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point.