We examine a relatively simple SU(2)-invariant model containing chiral three-spin interactions on a Kagome lattice of S=1/2 spins, and show that it can give rise to both a gapped topological and a gapless quantum spin liquid. The model can be obtained from a Hubbard model, where fluxes through the elementary triangles of the lattice give rise to the chiral spin term. Our arguments are rooted in a formulation in terms of network models of edge states and are backed up by a careful numerical analysis. For a uniform choice of chirality on the lattice, we realize the Kalmeyer-Laughlin state, i.e. a gapped topological spin liquid which is identified as the nu=1/2 bosonic Laughlin state. We numerically obtain a full characterization of the universal properties of the state, including the topological degeneracy, the gapless edge state and the anyonic bulk excitations. For staggered chiralities, a gapless spin liquid emerges which exhibits gapless spin excitations along lines in momentum space, a feature that we probe by studying quasi-two-dimensional systems of finite width. We thus provide a single, appealingly simple spin model (i) for what is probably the simplest realization of the Kalmeyer-Laughlin state to date, as well as (ii) for a non-Fermi...

The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at $\\nu=8$ and $12$, with experimentally-testable consequences. We show that this can occur in Abelian fractional quantum Hall states as well, with the simplest examples being at $\\nu=8/7, 12/11, 8/15, 16/5$. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. Edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, the bulk-edge correspondence is typically one-to-many; there ...

We consider the non-equilibrium dynamics of topologically ordered systems driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This dynamics exhibits scaling in the spirit of Kibble and Zurek but now {\\it without} the presence of symmetry breaking and a local order parameter. The late stages of the process are seen to exhibit a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase, a potentially interesting signature of topological order. We illustrate these phenomena in the context of particular phase transitions out of the abelian Z_2 topologically ordered phase of the toric code/Z_2 gauge theory, and the non-abelian SU(2)k ordered phases of the relevant Levin-Wen models.

The study of 4d and 5d transition metal oxides is interesting because these materials incorporate both strong spinorbit coupling and strong correlations, and consequently distinct physical properties and the tantalizing possibility of novel topological phases. The ab initio results show that Pr$_2$Ir$_2$O$_7$ is a strong candidate to the ideal Luttinger-Abrikosov-Benesvilavskii state, which has a quadratic band touching right at the Fermi level. The sensitive feature of the quadratic band touching state suggests that strain/pressure applied to the pyrochlore iridate thin films may produce a topological insulator. The ab initio results also show systematic trend of stronger order and gap with decreasing rare earth radius. Comparison of the theoretical work with recent experimental results will also be discussed.

The pyrochore iridates A2Ir2O7 (A = Y or lanthanide) have been proposed to host a variety of exotic ground states driven by the interplay between electronic correlations and strong spin-orbit coupling effects. This includes novel phases such as topological insulators, spin liquids, axion insulators, and Weyl semi-metals. The identification of such phases often hinges on the measurement of the magnetic excitation spectrum or dynamic structure factor, usually carried out by inelastic neutron scattering (INS). However, in the case of the pyrochlore iridates, this presents a serious experimental challenge, as the large neutron absorption cross section of Ir and small size of available single crystal samples combine to make conventional INS measurements largely unfeasible. Resonant inelastic x-ray scattering (RIXS) represents a promising alternative to INS, which provides an element-specific probe of elementary spin, charge, orbital, and lattice excitations. We have performed high-resolution Ir L3-edge RIXS measurements to investigate the characteristic excitation spectra of the pyrochlore iridates Eu2Ir2O7, Pr2Ir2O7, and Y2Ir2O7. These measurements reveal valuable information about both the magnetic excitations and ....

We show that fermionic systems can have edge phases with only bosonic low-energy edge excitations, and we generalize the relation between bulk topological spins and the central charge. We demonstrate that every fermionic topological phase can be represented as a bosonic topogical phase together with some number of filled Landau levels. In addition, our analysis shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers p, such that the topological spins of quasiparticles in that theory are the p^n-th roots of unity, for some n. This leads to a demonstration that all Abelian topological phases can be represented by U(1)^N Chern-Simons theory with particular K-matrices.

Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi2Sr2CaCu2O8+delta by Chatterjee et al. [Nature Physics 6, 99 (2010)], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the hot spots on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while several order-parameter susceptibilities investigated

We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum k⃗=0. This quadratic band touching is protected by symmetries. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistically large ring-exchange term.

We show that the current thermodynamic measurements in the superconducting phase of $\\mathrm{U}\\mathrm{Ru}_2\\mathrm{Si}_2$ are compatible with two distinct singlet chiral paired states $k_z(k_x \\pm i k_y)$ and $(k_x\\pm i k_y)^2$. Despite possessing similar low temperature thermodynamic properties, these two pairings are topologically distinguished by their respective orbital angular momentum projections along the c-axis, $m=\\pm 1$ and $m=\\pm 2$. The point nodes of these states act as the monopoles and the anti-monopoles of the Berry\'s gauge flux of charge $\\pm m$, which are separated in the momentum space along the $c$ axis. Consequently, the point nodes of $k_z(k_x+i k_y)$ and $(k_x \\pm ik_y)^2$ states respectively realize the Weyl and the double-Weyl fermions, with chemical potential exactly tuned at the Fermi point, due to the charge conjugation symmetry. Due to the nontrivial topology, there are chirally dispersing surface states, which lead to Fermi arc, anomalous spin and thermal Hall effects, and various magneto-electric effects. However, an unambiguous determination of the bulk invariant can only be achieved by probing the pairing symmetry via a corner Josephson junction measurement, and ...

We show the violation of the entanglement-area law for bosonic systems with gapless factorized energy dispersions on a N^d Cartesian lattice in d-dimension, e.g., the exciton Bose liquid in two dimension. We explicitly show that a belt subsystem with width L preserving translational symmetry along d-1 Cartesian axes has leading entanglement entropy (N^{d-1}/3)\\\\ln L. Using this result, the strong subadditivity inequality, and lattice symmetries, we bound the entanglement entropy of a rectangular subsystem from below and above showing a logarithmic violation of the area law. For subsystems with a single flat boundary we also bound the entanglement entropy from below showing a logarithmic violation, and argue that the entanglement entropy of subsystems with arbitrary smooth boundaries are similarly bounded.

We report a Determinant QMC investigation of the Knight shift anomaly observed in NMR experiments of heavy fermion materials. Knight shift is believed to originate in the different temperature dependence of the conduction electron and local moment components of the total susceptibility $\chi$. We quantify the behavior of $\chi_{cc}(T), \chi_{cf}(T),$ and $\chi_{ff}(T)$ in the framework of periodic Anderson model (PAM), focusing on the evolution with different degree of conduction electron-local moment hybridization. These results confirm several predictions of the two-fluid theory of the Knight shift anomaly, including the demonstration of a universal logarithmic divergence of the contribution of the heavy electrons to the Knight shift. This universal behavior, which occurs with decreasing temperature below $T^{\ast}$ in the paramagnetic state, agrees well with experimental findings, and indicates that different heavy fermion materials exhibit a common scaling, differing only in the coherence temperature scale, $T^{\ast}$.

We identify physically relevant, albeit lying off the beaten track, gravity models that may provide a holographic description of some prototypical non-Fermi liquid states of strongly correlated condensed matter systems. Specifically, we discuss prospective gravity duals of the ubiquitous models of non-relativistic fermions coupled to gauge fields and Dirac fermions with the Coulomb interactions.

We investigate the behavior of the Kondo singlet under a time-dependent excitation using a Single-Electron transistor (SET) , a voltage-controllable electron trap realized via gating of two-dimensional electron gas in a GaAs/AlGaAs heterostructure. We show that, at bias oscillation frequencies of order of the Kondo temperature divided by Planck's constant, f0= kTk/h, the time-averaged electron transport across the transistor becomes non-adiabatic. At frequencies f ~ f0, the zero-bias conductance of the SET exhibits a strong suppression as compared to adiabatic predictions, and the suppression weakens when f is tuned both below and above f0. We find a good qualitative agreement between the observations and the available theoretical predictions and suggest further experiments to further elucidate the role of the Kondo temperature as the universal dynamic energy scale.

More than half a century after first being proposed by Sir Nevill Mott, the deceptively simple question of whether the interaction-driven electronic metal-insulator transition may be continuous remains enigmatic. Recent experiments on two-dimensional materials suggest that when the insulator is a quantum spin liquid, lack of magnetic long-range order on the insulating side may cause the transition to be continuous, or only very weakly first order. Motivated by this, we examine an extended Hubbard model on a triangular strip geometry that we argue harbors a quantum phase transition between a metal and a gapless spin liquid characterized by a spinon Fermi sea, i.e., the ``spin Bose metal''. We solve this model using large-scale numerical simulations, and present evidence that the Mott transition is indeed continuous, of the Kosterlitz-Thouless type. These results may provide a rare insight into the development of Mott criticality in strongly interacting two-dimensional materials, and elucidates a mechanism by which spin-liquid phases are stabilized in the vicinity of such transitions.

We develop an analytical theory for treating thermal fluctuations in a compact U(1) lattice gauge theory for quantum spin ice. Starting from a U(1) quantum spin liquid ground state, thermal fluctuations of gauge fields reduce the length scale for the gauge-field coherence from an infinity at zero temperature to a finite value at finite temperatures. This produces a quantum-classical crossover when the gauge-field coherence length becomes compared to the thermal de-Broglie length. Effects of thermal fluctuations on the zero-temperature transition from the U(1) quantum spin-liquid to Higgs phase is also discussed. These results are compared to recent experimental findings from neutron-scattering, muon spin relaxation, and thermodynamic measurements on magnetic rare-earth (Yb, Pr, and Tb) pyrochlore oxides.

We explore physics of a 3D Fermi system near generalized Pomeranchuk instabilities using a tractable crossingsymmetric equation method. We investigate ferromagnetic, paramagnetic, and phase separation regions. We find that approach to one critical channel (spin or density) drives instabilities in other non-critical channels. We study causes and implications of this \"quantum multi-criticality\". It is found that a charge nematic instability may precede spin or density Pomeranchuk instabilities under certain conditions. Interplay of spin and density quantum fluctuations and pairing trends in such systems are studied. The results should of general relevance, and may also be of relevance to ferromagnetic superconductors.

Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting electrons to topologically nontrivial backgrounds such as in polyacetylene. Here we demonstrate that electronic fractionalization combining features of both these mechanisms occurs in noncoplanar itinerant magnetic systems, where integer quantum Hall physics arises from the coupling of electrons to the magnetic background. The topologically stable magnetic vortices in such systems carry fractional (in general irrational) electronic quantum numbers and exhibit Abelian anyonic statistics. We analyze the properties of these topological defects by mapping the distortions of the magnetic texture onto effective non-Abelian vector potentials. We support our analytical results with extensive numerical calculations.

I will present our recent work on quantum criticality in the (conducting) pyrochlore iridates in the context of the wide range of exotic phenomena that occur on the pyrochlore lattice, such as Coulombic quantum spin liquids and quantum order-by-disorder. I will discuss in detail the physics of the highly-unusual super-universal quantum critical point between a non-Fermi liquid and a Weyl semimetal (with Ising-like order) that we uncovered in a model relevant to the pyrochlore iridates. There, the fluctuations in the parent non-Fermi liquid phase compete with the fluctuations due to the coupling to the Ising order parameter. Remarkably, the fluctuations of both origins are of the same order of magnitude and the resulting quantum critical regime belongs to a unique, very large, universality class, genuinely different from those obtained by considering the effects of a single phenomenon. Moreover, the perturbative analysis is controlled, yielding better faith in the theory. I will describe the scaling laws and some unusual coefficients of many physical quantities, and provide a scheme to observe the quantum critical point in experiment. I will discuss further experimental consequences of our work, in particular in the context of Pr2Ir2O7, ...

Recently, it has been shown that in certain lattice systems, e.g. in a flat band with spin-orbit coupling and spin polarization, at commensurate fillings the ground state is a fractional quantum Hall state. The excitations of this state are anyons, and we explore what happens at incommensurate fillings, where doping the system is assumed to create a finite density of anyon excitations. The presence of the underlying lattice allows access to an entirely new regime where the anyon kinetic energy can be larger than the anyon interaction strength. This leads to an anyon gas which can condense to form a charged superfluid. Driven by repulsive interactions, this mechanism for superconductivity differs from the conventional one of electron pairing. We present three possible outcomes, the first two with intrinsic topological order, i.e. containing fractionalized quasiparticles; while the third has no fractionalized excitations similar to a BCS-type state.

In this decade, experimental development of cold atomic systems has stimulated theoretical study of superfluidity. For the two-component fermionic system with the strong attractive interaction between fermions, the normal phase shows pseudo-gap and the Fermi-liquid picture does not apply. In order to study such nonperturbative physics, we developed a new formalism of FRG. We show that our formalism can describe the BEC of composite bosons in terms of the original fermionic degrees of freedom in the deep BEC region of the BCS-BEC crossover.

We propose a new theoretical scheme to obtain novel gapless states in frustrated spin/boson systems by fractionalizing topological defects. We focus on 2D systems with global $U(1)$ symmetries (bosons or XY-spins), in which we fractionalize the vortices into gapless fermions. We give an example of such a scheme and interpret it as a critical phase in the vicinity of spin-nematic states. An explicit construction is given in an $XY$-spin-1 system on triangular lattice.

Recently, there is a considerable study on gapped symmetric phases of bosons that do not break any symmetry. Even without symmetry breaking, the bosons can still be in many exotic new states of matter, such as symmetry-protected trivial (SPT) phases which are short-range entangled and symmetry-enriched topological (SET) phases which are long-range entangled. It is well-known that \\emph{non-interacting fermionic topological insulators}....

We study the minimum quantum dimer model on the kagome lattice using zero temperature Green's function Monte Carlo method. In the "extreme quantum limit", the model hosts a large dimer liquid phase adjacent to two valence bond solid phases (VBS). The phase transition to one of the VBS is continuous, induced by vison condensation. The critical theory contains four real fields, predicted by a projective symmetry analysis. The critical point is likely controlled by a new universality class beyond the standard Landau theory of phase transition.

The fate of a hole injected in an antiferromagnet is an outstanding issue of strongly correlated physics. It provides important insights into doped Mott insulators closely related to high-temperature superconductivity. Here, we report a systematic numerical study of t-J ladder systems based on the density matrix renormalization group. It reveals a surprising result for the single hole’s motion in an otherwise well-understood undoped system. Specifically, we find that the common belief of quasiparticle picture is invalidated by the self-localization of the doped hole. In contrast to Anderson localization caused by disorders, the charge localization discovered here is an entirely new phenomenon purely of strong correlation origin. It results from destructive quantum interference of novel signs picked up by the hole, and since the same effect is of a generic feature of doped Mott physics, our findings unveil a new paradigm which may go beyond the single hole doped system.