We show that interactions in quantum spin liquids can result in non-Hermitian phenomenology that differs qualitatively from mean-field expectations. We demonstrate this in two prominent cases through the effects of phonons and disorder on a Kitaev honeycomb model. Using analytic and numerical calculations, we show the generic appearance of exceptional points and rings depending on the symmetry of the system. Their existence is reflected in dynamical observables including the dynamic structure function measured in neutron scattering. The results point to new phenomenological features in realizable spin liquids that must be incorporated into the analysis of experimental data and also indicate that spin liquids could be generically stable to wider classes of perturbations.
Non-hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a non-diagonalizable Jordan block. It is known that symmetries can enhance the abundance of exceptional points in non-interacting systems. Here, we investigate the fate of such symmetry protected exceptional points in the presence of a symmetry preserving interaction between fermions and find that, (i) exceptional points are stable in the presence of the interaction. Their propagation through the parameter space leads to the formation of characteristi…
We show the existence of non-Hermitian degeneracies, known as exceptional points, in the collective mode spectrum of Fermi liquids with quadrupolar interactions. Through a careful analysis of the analytic properties of the dynamic quadrupolar susceptibility, we show that, in the weak attractive region, two stable collective modes coalesce to an exceptional point. We completely characterize this singularity, explicitly showing its topological properties. Experimental signatures are also discussed.
We establish the appearance of a qualitatively new type of spin liquid with emergent exceptional points when coupling to the environment. We consider an open system of the Kitaev honeycomb model generically coupled to an external environment. In extended parameter regimes, the Dirac points of the emergent Majorana fermions from the original model are split into exceptional points with Fermi arcs connecting them. In glaring contrast to the original gapless phase of the honeycomb model which requires time-reversal symmetry, this new phase is stable against all perturbations. The system also disp…
Exceptional points, which are topological non-Hermitian degeneracies, show up in the collective mode spectrum of Fermi Liquids with high angular momentum interactions. In this paper, we look for signatures of these non-trivial singularities by computing the AC conductivity of Fermi liquids with dipolar and quadrupolar interactions in a narrow slab. We show that the finite size of the slab imprints clear signatures of the structures of the collective mode spectrum in the conductivity as well as in the dephasing between the electric field and the current density in a wide range of coupling const…
We report on the dynamical formation of exceptional degeneracies in basic correlation functions of non-integrable one- and two-dimensional systems quenched to the vicinity of a critical point. Remarkably, fine-tuned semi-metallic points in the phase diagram of the considered systems are thereby promoted to topologically robust non-Hermitian (NH) nodal phases emerging in the coherent long-time evolution of a dynamically equilibrating system. In the framework of non-equilibrium Green's function methods within the conserving second Born approximation, we predict observable signatures of these nov…
Despite recent extensive studies of the non-Hermitian topology, understanding interaction effects is left as a crucial question. In this paper, we address interaction effects on exceptional points which are protected by the non-trivial point-gap topology unique to non-Hermitian systems. Our analysis in a two-dimensional parameter space elucidates the existence of exceptional points and symmetry-protected exceptional rings fragile against interactions; they are topologically protected only in non-interacting cases. This fragility of exceptional points and symmetry-protected exceptional rings ar…
Introducing both Berry curvature and chiral anomaly into Landau's Fermi-liquid theory, we construct a topological Fermi-liquid theory, applicable to interacting Weyl metals in the absence of time reversal symmetry. Following the Landau's Fermi-liquid theory, we obtain an effective free-energy functional in terms of the density field of chiral fermions. The density field of chiral fermions is determined by a self-consistent equation, minimizing the effective free-energy functional with respect to the order-parameter field. Beyond these thermodynamic properties, we construct Boltzmann transport …
We study the Fermi surface topological transition of the pocket-opening type in a two dimensional Fermi liquid with spin-orbit coupling of Rashba type. We find that the interactions, far from instabilities, drive the transition first order at zero temperature surprisingly in a more pronounced way than in the case of interacting Fermi liquid without spin-orbit coupling. We first gain insight from second order perturbation theory in the self-energy. We then extend the results to stronger interaction, using the self-consistent fluctuation approximation. We discuss existing experimental work on th…
We study a strongly interacting, fermionic fluid in the presence of an applied magnetic field using a holographic framework. At low temperatures, translation symmetry is spontaneously broken and the resulting phase is a striped Hall fluid. Due to the magnetic field, an electric field applied parallel to the stripes causes the stripes to slide, a phenomenon we coin "Hall sliding." We also investigate the magneto-transport of the system in the presence of an explicit translation symmetry-breaking lattice which pins the stripes. Electrical properties are well represented by a hydrodynamical model…
Instead of solving Dirac (or Klein-Gordon) equation for a many body system, in this paper a variational method has been used to investigate the properties of two dimensional (2D) strongly interacting fermions and the results have been applied to 2D liquid $^3He$ as the only real fermion system. Our results show that this variational method, known as lowest order constrained variational method, can be used to relativistic 2D fermion systems with a good accuracy. In the case of 2D liquid $^3He$, Our calculations showed that at higher temperatures relativistic effects are more significant and qua…
The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynam…
We address the emergent quantum critical phenomena for (pseudo)spin-3/2 birefringent fermions, featuring two effective Fermi velocities, when they reside close to itinerant Mott transitions realized through spontaneous symmetry breaking and triggered by strong local or Hubbardlike repulsive interactions. Irrespective of the nature of the mass orderings that produce fully gapped quasiparticle spectra in the ordered phase, which otherwise can be grouped into three classes, the system always possesses a \emph{unique} terminal velocity near the corresponding quantum critical point. The associated …
Optical conductivity (OC) can serve as a measure of correlation effects in a wide range of condensed matter systems. We here show that the long-range tail of the Coulomb interaction yields a universal correction to the OC in a three-dimensional Weyl semimetal $σ(Ω)=σ_0(Ω)\left[ 1+\frac{1}{N+1} \right]$, where of $σ_0(Ω)=Ne^2_0 Ω/(12 h v)$ is the OC in the non-interacting system, with $v$ as the actual (renormalized) Fermi velocity of Weyl quasiparticles at frequency $Ω$, and $e_0$ is the electron charge in vacuum. Such universal enhancement of OC, which depends only on the number of Weyl nodes…
We present a new method for calculating Renyi entanglement entropies for fermionic field-theories originating from microscopic Hamiltonians. The method builds on an operator identity which we discover for the first time. The identity leads to the representation of traces of operator products, and thus Renyi entropies of a subsystem, in terms of fermionic-displacement operators. This allows for a very transparent path-integral formulation, both in and out-of-equilibrium, having a simple boundary condition on the fermionic fields. The method is validated by reproducing well known expressions for…
We study a problem of interacting fractional charges with $J_1$-$J_2$-$J_3$ Ising model on a checkerboard lattice under magnetic field. As a result of the interplay between repulsive interactions and particle density tuning by magnetic field, the fractional charges form a classical spin liquid (CSL) phase. The CSL phase is composed of degenerate spin configurations, which can be mapped to the trimer covering of dual square lattice. The CSL state shows macroscopic ground-state entropy, implying the emergence of novel quantum spin liquid phase when quantum fluctuations are turned on. In addition…
We demonstrate that the plasmon in one-dimensional Coulomb interacting electron fluids can develop a finite-momentum maxon-roton-like nonmonotonic energy-momentum dispersion. Such an unusual nonmonotonicity arises from the strongly interacting $1/r$ Coulomb potential going beyond the conventional band linearization approximation used in the standard bosonization theories of Luttinger liquids. We provide details for the nonmonotonic plasmon dispersion using both bosonization and RPA theories. We also calculate the specific heat including the nonmonotonicity and discuss possibilities for observi…
We report experimental verification of the recently predicted collective modes of spinons, stabilized by backscattering interaction, in a model quantum spin chain material. We exploit the unique geometry of uniform Dzyaloshinskii-Moriya interactions in K$_2$CuSO$_4$Br$_2$ to measure the interaction-induced splitting between the two components of the electron spin resonance (ESR) response doublet. From that we directly determine the magnitude of the "marginally irrelevant" backscattering interaction between spinons for the first time.
We consider the response of the density of a fermion ensemble to an applied weak static magnetic field. It is known that for non-interacting 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 Fermi liquid and 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 study the ground state phase diagram of a one-dimensional hard-core bosonic model with nearest-neighbor interactions (XXZ model) where every site is coupled Ohmically to an independent but identical reservoir, hereby generalizing spin-boson models to interacting spin-boson systems. We show that a bath-induced Bose metal phase can occur in the ground state phase diagram away from half filling. This phase is compressible, gapless, and conducting but not superfluid. At haf-filling, only a Luttinger liquid and a charge density wave are found. The phase transition between them is of Kosterlitz-T…
We present a mapping of a two-dimensional system of interacting bosons in a strong perpendicular magnetic field to an equivalent system of interacting bosons on the square lattice in the absence of the field. The mapping utilizes a magnetic Bloch and the corresponding magnetic Wannier single-particle basis in the lowest Landau level. By construction, the ground states of the resulting model of interacting bosons on the square lattice are gapped fractionalized liquids or gapless Bose metal states with broken time reversal symmetry at specific rational filling fractions.
We provide strong evidence of a quantum critical point (QCP) associated with the destruction of Kondo screening in the Anderson-Hubbard model for interacting electrons with quenched disorder. A unique crossover energy scale, $ω^*$ separating the Fermi liquid and non-Fermi liquid (nFL) scattering dynamics on the metallic side of the quantum critical fan is identified. The scale vanishes at the disorder driven QCP. We interpret our results by measuring the distribution of Kondo scales and find that the QCP occurs when this distribution acquires a finite intercept, indicating a Kondo destruction …
We present the quantum critical theory of an interacting nodal Fermi-liquid of quasi-relativisitc pseudo-spin-3/2 fermions that have a non-interacting birefringent spectrum with two distinct Fermi velocities. When such quasiparticles interact with gapless bosonic degrees of freedom that mediate either the long-range Coulomb interaction or its short range component (responsible for spontaneous symmetry breaking), in the deep infrared or quantum critical regime in two dimensions the system is respectively described by a marginal- or a non-Fermi liquid of relativistic spin-1/2 fermions (possessin…
We show how a ground state trial wavefunction of a Fermi liquid can be systematically improved introducing a sequence of renormalized coordinates through an iterative backflow transformation. We apply this scheme to calculate the ground state energy of liquid $^3$He in two dimensions at freezing density using variational and fixed-node diffusion Monte Carlo. Comparing with exact transient estimate results for systems with small number of particles, we find that variance extrapolations provide accurate results for the true ground state together with stringent lower bounds. For larger systems th…
We consider a helical spin liquid system which shows majorana fermion modes at the edge. The interaction between the quasiparticles in this system induces phase transition, Majorana-Ising transition. We comply the density matrix renormalization group method to study this phase transition for the entire regime of the parameter space. We observe the presence of topological quantum phase transition for repulsive interaction, however this phase is more stable for the attractive interaction. The length scale dependent study shows many new and important results and we show explicitly that the major …
Landau-Fermi liquid theory is conventionally believed to hold whenever the interacting single-particle density of states develops a $δ$-like component at the Fermi surface, which is associated with quasiparticles. Here we show that a microscopic justification can be actually achieved under more general circumstances, even in case coherent quasiparticles are totally missing and the interacting single-particle density of states vanishes at the chemical potential as consequence of a pole singularity in the self-energy.
Interacting fermion systems in one dimension, which in the low energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional exchange statistics. This is shown by use of Landau's Fermi liquid theory, with quasiparticles interpreted as adiabatically dressed fermions. An application of this method is included, where boundary excitations of a two-dimensional quantum Hall electron system are studied.
We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated "tomographic" transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless…
We analyze a zero-dimensional correlated system with special emphasis on the non-Hermitian point-gap topology protected by chiral symmetry. Our analysis elucidates that correlations destroy an exceptional point on a topological transition point which separates two topological phases in the non-interacting case; one of them is characterized by the zero-th Chern number $N_{0\mathrm{Ch}}=0$, and the other is characterized by $N_{0\mathrm{Ch}}=2$. This fact implies that correlations allow to continuously connect the two distinct topological phases in the non-interacting case without closing the po…
An unbiased zero-temperature auxiliary-field quantum Monte Carlo method is employed to analyze the nature of the semimetallic phase of the two-dimensional Hubbard model on the honeycomb lattice at half filling. It is shown that the quasiparticle weight $Z$ of the massless Dirac fermions at the Fermi level, which characterizes the coherence of zero-energy single-particle excitations, can be evaluated in terms of the long-distance equal-time single-particle Green's function. If this quantity remains finite in the thermodynamic limit, the low-energy single-particle excitations of the correlated s…
The concept of Fermi liquid lays a solid cornerstone to the understanding of electronic correlations in quantum matter. This ordered many-body state rigorously organizes electrons at zero temperature in progressively higher momentum states, up to the Fermi surface. As such, it displays rigidity against perturbations. Such rigidity generates Fermi-surface resonances which manifest as longitudinal and transverse collective modes. Although these Fermi-liquid collective modes have been analyzed and observed in electrically neutral liquid helium, they remain unexplored in charged solid-state system…
A highlight of Fermi-liquid phenomenology, as explored in neutral $^3$He, is the observation that in the collisionless regime shear stress propagates as if one is dealing with the transverse phonon of a solid. The existence of this $"$transverse zero sound$"$ requires that the quasiparticle mass enhancement exceeds a critical value. Could such a propagating shear stress also exist in strongly correlated electron systems? Despite some noticeable differences with the neutral case in the Galilean continuum, we arrive at the verdict that transverse zero sound should be generic. We present an exper…
