Conformal Field Theory on the Fermi Surface

Stress tensor and current correlators of interacting conformal field theories in 2+1 dimensions: Fermionic Dirac matter coupled to U(1) gauge field

We compute the central charge $C_T$ and universal conductivity $C_J$ of $N_F$ fermions coupled to a $U(1)$ gauge field up to next-to-leading order in the $1/N_F$ expansion. We discuss implications of these precision computations as a diagnostic for response and entanglement properties of interacting conformal field theories for strongly correlated condensed matter phases and conformal quantum electrodynamics in $2+1$ dimensions.

Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories

We systematically study the exclusion statistics for quasi-particles for Conformal Field Theory spectra by employing a method based on recursion relations for truncated spectra. Our examples include generalized fermions in c<1 unitary minimal models, Z_k parafermions, and spinons for the su(n)_1, so(n)_1 and sp(2n)_1 Wess-Zumino-Witten models. For some of the latter examples we present explicit expressions for finitized affine characters and for the N-spinon decomposition of affine characters.

Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach

The physical properties of arbitrary half-integer spins F = N - 1/2 fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for F \ge 3/2: A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of Z_N parafermionic degrees of freedom. The quantum phase transition for F=3/…

在模糊球上自由和相互作用费米共形场论

Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere

本文研究在模糊球上自由和相互作用费米共形场论，通过局部费米算子和角动量不匹配实现相变，并发现超Ising理论的超共形对称性。

Chiral correlators of the Ising conformal field theory

We derive explicit expressions for the conformal blocks of the Ising conformal field theory, for the correlators of an arbitrary number of primary fields. These results are obtained from the bosonized description of the Ising model. Interestingly, correlators involving Majorana fermions, can be obtained in two different ways, giving rise to identities between the `bosonic' and `fermionic' description of these correlators. These identities are generalizations of the famous Cauchy-identity. The conformal blocks of the Ising model are used to derive expression for the conformal blocks of the su(2…

边界共形场论中的费米子：交叉对称性与$ε$展开

Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $ε$-Expansion

本文利用运动方程与交叉对称性约束相互作用费米子边界共形场论，首次推导体旋量共形块，计算了多种维度下耦合的新反常维数，并关联了表面算符反常维数与电荷密度行为。

二次能带交叉中的$c=-2$共形场论

$c=-2$ conformal field theory in quadratic band touching

针对二次能带交叉量子临界点表征不完善的问题，本研究建立其自由费米子模型与辛费米子理论的对应，发现二维下对应$c=-2$对数共形场论，识别出无隙系统中的任意子激发及相关拓扑特性。

Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces

We show that quantum Hall states on surfaces with conical singularities behave as conformal primaries near the singular points, with a conformal dimension controlled by the gravitational anomaly. We show that the electronic fluid at the cone tip possesses an intrinsic angular momentum equal to the conformal dimension, in units of the Planck constant. Finally, we argue that the gravitational anomaly also controls { the fine structure of electronic density at the tip, and } the exchange statistics of cones in the Laughlin states, arising from adiabatically braiding conical singularities. Thus, t…

QED$_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning

We construct a conformal lattice theory with only gauge degrees of freedom based on the induced non-local gauge action in QED$_3$ coupled to large number of flavors $N$ of massless two-component Dirac fermions. This lattice system displays signatures of criticality in gauge observables, without any fine-tuning of couplings and can be studied without Monte Carlo critical slow-down. By coupling exactly massless fermion sources to the lattice gauge model, we demonstrate that non-trivial anomalous dimensions are induced in fermion bilinears depending on the dimensionless electric charge of the fer…

费米点拓扑决定扩展量子自旋链中的涌现共形临界性

Fermi-Point Topology Determines Emergent Conformal Criticality in Extended Quantum Spin Chains

该研究在含竞争相互作用等的扩展量子自旋链中，建立费米点拓扑与涌现共形场论的微观关联，揭示 Lifshitz 转变可产生多类中心荷的共形临界相及非常规多临界行为。

Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of nu = 1/(2p+1) quantum Hall sequences

We present a comprehensive study of the effective Conformal Field Theory (CFT) describing the low energy excitations of a gas of spinless interacting fermions on a circle in the gapless regime (Luttinger liquid). Functional techniques and modular transformation properties are used to compute all correlation functions in a finite size and at finite temperature. Forward scattering disorder is treated exactly. Laughlin experiments on charge transport in a Quantum Hall Fluid on a cylinder are reviewed within this CFT framework. Edge excitations above a given bulk excitation are described by a twis…

Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases

Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT…