We consider the response of the density of a fermion ensemble to an applied weak static magnetic field. It is known that, for a noninteracting Fermi gas, this response is fully characterized by the Fermi volume and the Berry curvature on the Fermi surface. Here we show the same result holds for interacting fermions, including a Fermi liquid and a non-Fermi liquid, to all orders in perturbation theory. Our result relies only on the assumption of a well-defined Fermi surface and the general analytic properties of quantum field theory, and is completely model independent.We consider the response of the density of a fermion ensemble to an applied weak static magnetic field. It is known that, for a noninteracting Fermi gas, this response is fully characterized by the Fermi volume and the Berry curvature on the Fermi surface. Here we show the same result holds for interacting fermions, including a Fermi liquid and a non-Fermi liquid, to all orders in perturbation theory. Our result relies only on the assumption of a well-defined Fermi surface and the general analytic properties of quantum field theory, and is completely model independent.

arXiv:1704.04241Physical Review LettersAug 31, 20174 citations

Tractable model for a fractionalized Fermi liquid (FL $^*$ ) on a square latticeTractable model for a fractionalized Fermi liquid (FL$^*$) on a square lattice

Piers Coleman, Elio J. König, Aaditya Panigrahi +1 more

Motivated by the continued interest in Fermi-surface reconstruction without symmetry breaking, we present an analytically tractable microscopic model of a fractionalized Fermi liquid (FL $^*$ ) on a square lattice and discuss its potential relevance to the cuprates. As in ancilla-qubit constructions, the model is related to Kondo lattice systems, but in this case, the conduction electrons interact with a $\mathbb{Z}_2$ spin liquid of the Yao--Lee type, with a Majorana Fermi surface. The associated $\mathbb Z_2$ gauge theory is static so that the model can be analytically solved to leading-logarithic accuracy. There are two phases: one in which the fractionalized fermions of the spin liquid hybridize with conduction electrons to form a common Fermi surface violating the naive Luttinger count, and one in which they remain decoupled. We discuss the salient features of the small Fermi-surface phase, including analytically derived momentum dependent coherence factors responsible for the appearance of Fermi arcs à la Yang-Rice-Zhang. We further discuss the impact of quantum and thermal fluctuations, including a strong diamagnetic response and a logarithmically divergent Sommerfeld coefficient at the onset of the pseudogap.Motivated by the continued interest in Fermi-surface reconstruction without symmetry breaking, we present an analytically tractable microscopic model of a fractionalized Fermi liquid (FL$^*$) on a square lattice and discuss its potential relevance to the cuprates. As in ancilla-qubit constructions, the model is related to Kondo lattice systems, but in this case, the conduction electrons interact with a $\mathbb{Z}_2$ spin liquid of the Yao--Lee type, with a Majorana Fermi surface. The associated $\mathbb Z_2$ gauge theory is static so that the model can be analytically solved to leading-logarithic accuracy. There are two phases: one in which the fractionalized fermions of the spin liquid hybridize with conduction electrons to form a common Fermi surface violating the naive Luttinger count, and one in which they remain decoupled. We discuss the salient features of the small Fermi-surface phase, including analytically derived momentum dependent coherence factors responsible for the appearance of Fermi arcs à la Yang-Rice-Zhang. We further discuss the impact of quantum and thermal fluctuations, including a strong diamagnetic response and a logarithmically divergent Sommerfeld coefficient at the onset of the pseudogap.

arXiv:2604.06157Apr 7, 20260 citations

Fermi surface fluctuations and breakdown of Fermi liquid behavior

Walter Metzner, Luca Dell’Anna

Physica C SuperconductivityMar 29, 20070 citations

Dynamics of fermi liquids

Jagdish Prasad Singh

Jun 30, 19830 citations

Nonlinear optical conductivity of U(1) spin liquids with large spinon Fermi surfaces

Yuan-Fei Ma, Tai Kai Ng

In this paper we study the nonlinear current response of $U(1)$ spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field $\mathbf{E}(t)$ within the framework of an effective $U(1)$ gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law $(\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\eta}})$ response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency $3\ensuremath{\omega}$ inside the spin liquids.In this paper we study the nonlinear current response of $U(1)$ spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field $\mathbf{E}(t)$ within the framework of an effective $U(1)$ gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law $(\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\eta}})$ response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency $3\ensuremath{\omega}$ inside the spin liquids.

arXiv:1503.05731Physical review. B./Physical review. BJun 6, 20162 citations

Tractable model for a fractionalized Fermi liquid (FL

^*

) on a square lattice

Motivated by the continued interest in Fermi-surface reconstruction without symmetry breaking, we present an analytically tractable microscopic model of a fractionalized Fermi liquid (FL

^*

) on a square lattice and discuss its potential relevance to the cuprates. As in ancilla-qubit constructions, the model is related to Kondo lattice systems, but in this case, the conduction electrons interact with a

\mathbb{Z}_2

spin liquid of the Yao--Lee type, with a Majorana Fermi surface. The associated

\mathbb Z_2

gauge theory is static so that the model can be analytically solved to leading-logarithic accuracy. There are two phases: one in which the fractionalized fermions of the spin liquid hybridize with conduction electrons to form a common Fermi surface violating the naive Luttinger count, and one in which they remain decoupled. We discuss the salient features of the small Fermi-surface phase, including analytically derived momentum dependent coherence factors responsible for the appearance of Fermi arcs à la Yang-Rice-Zhang. We further discuss the impact of quantum and thermal fluctuations, including a strong diamagnetic response and a logarithmically divergent Sommerfeld coefficient at the onset of the pseudogap.

In this paper we study the nonlinear current response of

U(1)

spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field

\mathbf{E}(t)

within the framework of an effective

U(1)

gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law $(\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\eta}})$ response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency $3\ensuremath{\omega}$ inside the spin liquids.