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arXiv:1112.6243

Two-dimensional confinement of critical U(1) gauge field in the presence of Fermi surface

Yin Zhong, Ke Liu, Yong‐Qiang Wang, Hong‐Gang Luo

Published Dec 29, 2011• 0 citations
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Abstract

The compact U(1) gauge field occurs in many fractionalized descriptions of low dimensional quantum magnetism and heavy fermion systems. In this respect a fundamental question about the gauge field is whether it is confined or not in the presence of Fermi surface. In this paper we show that the U(1) gauge field with a possible positive anomalous dimension in the presence of Fermi surface has to be in the confined state, although it is strongly coupled to abundant gapless fermionic excitations near the Fermi surface in two spatial dimensions. This means that some quantum spin liquids and/or fractionalized metallic states described in terms of this kind of gauge fields with positive anomalous dimensions are unstable to other possible symmetry-breaking states, as a result, they are not be appropriate candidates for ground states in related systems. The instability obtained shows some novel features of the quantum spin liquids and/or fractionalized metallic states in the presence of Fermi surface which have not been reported in the literature. The result could be useful for further study in the quantum spin liquids and many related slave-particle gauge theories in strongly correlated electron systems.

DOI
10.48550/arxiv.1112.6243

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The compact U(1) gauge field occurs in many fractionalized descriptions of low dimensional quantum magnetism and heavy fermion systems. In this respect a fundamental question about the gauge field is whether it is confined or not in the presence of Fermi surface. In this paper we show that the U(1) gauge field with a possible positive anomalous dimension in the presence of Fermi surface has to be in the confined state, although it is strongly coupled to abundant gapless fermionic excitations near the Fermi surface in two spatial dimensions. This means that some quantum spin liquids and/or fractionalized metallic states described in terms of this kind of gauge fields with positive anomalous dimensions are unstable to other possible symmetry-breaking states, as a result, they are not be appropriate candidates for ground states in related systems. The instability obtained shows some novel features of the quantum spin liquids and/or fractionalized metallic states in the presence of Fermi surface which have not been reported in the literature. The result could be useful for further study in the quantum spin liquids and many related slave-particle gauge theories in strongly correlated electron systems.
Many popular models of fractionalized spin liquids contain neutral fermionic spinon excitations on a Fermi surface, carrying unit charges under a compact U(1) gauge force. We argue that except at possible critical points, instanton effects generically render such states unstable to confinement in two spatial dimensions, so that all elementary excitations are gauge neutral, and there is no spinon Fermi surface. Similar results are expected to apply to SU(2) spin liquids. However, fractionalized states can appear when the gauge symmetry is broken down to a discrete subgroup by the Higgs mechanism. Our argument generalizes earlier results on confinement in the pure gauge theory, and arguments for the instability of the U(1) ``staggered flux'' and ``algebraic'' spin liquids with a Dirac spectrum for fermionic spinons.
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.
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 (QED3)({\mathrm{QED}}_{3})(QED3​) 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 eee [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 NNN of massless Dirac fermions in QED3{\mathrm{QED}}_{3}QED3​. 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.
We study the low-energy effective theory for a non-Fermi-liquid state in 2+12+12+1 dimensions, where a transverse U(1) gauge field is coupled with a patch of Fermi surface with NNN flavors of fermion in the large NNN limit. In the low-energy limit, quantum corrections are classified according to the genus of the two-dimensional surface on which Feynman diagrams can be drawn without a crossing in a double line representation and all planar diagrams are important in the leading order. The emerging theory has the similar structure to the four-dimensional SU(N) gauge theory in the large NNN limit. Because of strong quantum fluctuations caused by the abundant low-energy excitations near the Fermi surface, low-energy fermions remain strongly coupled even in the large NNN limit. As a result, there are infinitely many quantum corrections that contribute to the leading frequency dependence of the Green's function of fermion on the Fermi surface. On the contrary, the boson self-energy is not modified beyond the one-loop level and the theory is stable in the large NNN limit. The nonperturbative nature of the theory also shows up in correlation functions of gauge-invariant operators.
We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.
Deconfined quantum critical points have attracted lots of attention in the past decades but were mainly restricted to incompressible phases. On the other hand, various experimental puzzles call for a new theory of unconventional quantum criticality between metals at a generic density. Here we explore the possibility of a deconfined transition between two symmetric Fermi liquids (FLs) in a bilayer model tuned by interlayer antiferromagnetic spin-spin coupling ${J}_{\ensuremath{\perp}}$. Across the transition the Fermi-surface volume per flavor jumps by 1/21/21/2 of the Brillouin zone, similar to the small to large Fermi-surface transitions in heavy fermion systems and maybe also in the high Tc{T}_{\text{c}}Tc​ cuprates. But in the bilayer case the small Fermi-surface phase (dubbed sFL) has neither symmetry breaking nor fractionalization, akin to the symmetric mass generation discussed in high-energy physics. We formulate a deconfined critical theory where the two Fermi liquids correspond to Higgs and/or confined phases of a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ gauge theory. We show that this deconfined FL to FL transition fixed point is unstable to pairing and thus a superconductor dome is expected at low temperature. At finite temperature above the pairing scale, microscopic electron is a composite of three deconfined fractional fermions in the critical theory. We also introduce another parameter which can suppress the pairing instability, leading to a deconfined phase stable to zero temperature. Our work opens a direction to exploring deconfined metallic criticality and pairing mechanism from critical gauge field. The transition may be relevant to the recently found nickelate superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ and future experiments in bilayer optical lattice.