Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed.Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed.

arXiv:2107.00661Physical review. B./Physical review. BOct 20, 20219 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

Conduction properties of strongly interacting Fermions

Jean-Philippe Brantut

Bulletin of the American Physical SocietyMar 21, 20130 citations

Dynamics of fermions coupling to a U(1) gauge field in the limit e 2

Ng T-K

Physical Review BJan 1, 20010 citations

({\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.