Hitherto, the discrete identification of quantum spin liquid phase, holy grail of condensed matter physics, remains a challenging task experimentally. However, the precursor of quantum spin liquid state may reflect in the spin dynamics even in the paramagnetic phase over a wide temperature range as conjectured theoretically. Here we report comprehensive inelastic light (Raman) scattering measurements on the Ir based double perovskite, Gd2ZnIrO6, as a function of different incident photon energies and polarization in a broad temperature range. Our results evidenced the spin fractionalization within the paramagnetic phase reflected in the emergence of a polarization independent quasi-elastic peak at low energies with lowering temperature. Also, the fluctuating scattering amplitude measured via dynamic Raman susceptibility increases with lowering temperature and decreases mildly upon entering into long-range magnetic ordering phase, below 23 K, suggesting the magnetic origin of these fluctuations. This anomalous scattering response is thus indicative of fluctuating fractional spin evincing the quantum spin liquid phase in a three-dimensional double perovskite system.
In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$1/2$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped $\mathbb{Z_2}$ spin liquids.
In this work we study symmetry fractionalization of vison excitations in topological $\mathbb{Z}_2$ spin liquids. We show that in the presence of the full $\mathrm{SO}(3)$ spin rotational symmetry and if there is an odd number of spin-$\frac12$ per unit cell, the symmetry fractionalization of visons is completely fixed. On the other hand, visons can have different classes of symmetry fractionalization if the spin rotational symmetry is reduced. As a concrete example, we show that visons in the Balents-Fisher-Girvin $\mathbb{Z}_2$ spin liquid have crystal symmetry fractionalization classes whic…
In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different topologically ordered spin liquid states. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected $\mathbb Z_2$ spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can…
In this work we study the crystal symmetry fractionalization in chiral spin liquids with the chiral-semion topological order. We show that if such a chiral spin liquid is realized in a two-dimensional lattice model with odd number of spin-$\frac12$ per unit cell and the state preserves spin rotation symmetry and translation symmetries, the semion excitation must carry both half-integer spin and fractional crystal quantum numbers. As a result, only a unique symmetry enriched topological phase can be realized in chiral spin liquids in a spin-$\frac12$ kagome lattice model. These fractional symme…
Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for \textit{classical} Heisenberg models, only one kind of fractionalised spin liquid phase, the so-called Coulomb or $U(1)$ spin liquid, has until recently been identified: this exhibits algebraic spin correlations and impurity moments, `orphan spins', whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalisation in combination with exponentially decaying correlations. These can be thou…
The standard theoretical approach to gapless spin liquid phases of two-dimensional frustrated quantum antiferromagnets invokes the concept of fermionic slave particles into which the spin fractionalizes. As an alternate we explore new kinds of gapless spin liquid phases in frustrated quantum magnets with XY anisotropy where the vortex of the spin fractionalizes into gapless itinerant fermions. The resulting gapless fractionalized vortex liquid phases are studied within a slave particle framework that is dual to the usual one. We demonstrate the stability of some such phases and describe their …
We propose a hierarchy of spin liquids with spin S, which are generated via a Schwinger boson projection from 2S (Abelian) chiral spin liquids with S=1/2. We argue that the P and T invariant liquids we construct for integer spin S support SU(2) level k=S non-Abelian statistics. We conjecture that these spin liquids serve as paradigms for antiferromagnets which are disordered through mobile charge carriers.
Excitations which carry "fractional" quantum numbers are known to exist in one dimension in polyacetylene, and in two dimensions, in the fractional quantum Hall effect. Fractional excitations have also been invoked to explain the breakdown of the conventional theory of metals in a wide range of three-dimensional materials. However the existence of fractional excitations in three dimensions remains highly controversial. In this Letter we report direct numerical evidence for the existence of a quantum liquid phase supporting fractional excitations in a concrete, three-dimensional microscopic mod…
We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological quantum field theories that encode the Abelian fractional quantum Hall liquids. We explain the hierarchical construction of such a theory and establish for it a bulk-edge correspondence by deriving the equivalent edge theory for chiral bosonic fields. Further, we compute the Fermi-Bose correlation functions of the edge theory and provide representative ground state wave functions for systems described…
Motivated by spin-wave continuum (SWC) observed in recent neutron scattering experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to study dynamic spin structure factor $S(\mathbf{q},ω)$ of spin liquid states on the kagome lattice. Spin-1 excited states in spin liquids are represented by Gutzwiller-projected two-spinon excited wave functions. We investigate three different spin liquid candidates, spinon Fermi-surface spin liquid (FSL), Dirac spin liquid (DSL) and random-flux spin liquid (RSL). FSL and RSL have low energy peaks in $S(\mathbf{q},ω)$ at $K$ points in the ext…
We study the interplay of confining potential, electron-electron interaction, and Zeeman splitting at the edges of fractional quantum Hall liquids, using numerical diagonalization of finite-size systems. The filling factors studied include 1/3, 5/2, 2/5, and 2/3. In the absence of Zeeman splitting and an edge, the first two have spin fully polarized ground states, while the latter two have singlet ground states. We find that with few exceptions, edge instabilities of these systems are triggered by softening of edge spin waves for Abelian fractional quantum Hall liquids (1/3, 2/5 and 2/3 liquid…
The chiral Luttinger liquid theory for fractional quantum Hall edge transport predicts universal power-law behavior in the current-voltage ($I$-$V$) characteristics for electrons tunneling into the edge. However, it has not been unambiguously observed in experiments in two-dimensional electron gases based on GaAs/GaAlAs heterostructures or quantum wells. One plausible cause is the fractional quantum Hall edge reconstruction, which introduces non-chiral edge modes. The coupling between counterpropagating edge modes can modify the exponent of the $I$-$V$ characteristics. By comparing the $ν=1/3$…
Inspired by the recent discovery of superconductivity in the nickelate Nd$_{1-x}$Sr$_x$NiO$_2$, we study a generalized $t-J$ model to investigate the correlated phases induced by doping spin-one Ni$^{2+}$ into a spin $1/2$ Mott insulator formed by Ni$^{1+}$. Based on a three-fermion parton mean field analysis, we identify a robust fractional Fermi liquid (FL*) phase for almost every doping level. The FL* state is characterized by a small Fermi pocket on top of a spin liquid, which violates the Luttinger theorem of a conventional Fermi liquid and is an example of a symmetric pseudogap metal. Fu…
In this work we explore experimental signatures of fractional topological insulators in three dimensions. These are states of matter with a fully gapped bulk that host exotic gapless surface states and fractionally charged quasiparticles. They are partially characterized by a non-trivial magneto-electric response while preserving time reversal. We describe how these phases appear in a variety of probes including photoemmission, tunneling, and quantum oscillations. We also discuss the effects of doping and proximate superconductivity. We argue that despite our current theoretical inability to p…
We consider gapped Z2 spin liquids, where spinon quasiparticles may carry fractional quantum numbers of space group symmetry. In particular, spinons can carry fractional crystal momentum. We show that such quantum number fractionalization has dramatic, spectroscopically accessible consequences, namely enhanced periodicity of the two-spinon density of states in the Brillouin zone, which can be detected via inelastic neutron scattering. This effect is a sharp signature of certain topologically ordered spin liquids and other symmetry enriched topological phases. Considering square lattice space g…
We describe ground states of correlated electron systems in which the electron fractionalizes into separate quasiparticles which carry its spin and its charge, and into real Majorana fermions which carry its Fermi statistics. Such parent states provide a unified theory of previously studied fractionalized states: their descendants include insulating and conducting states with neutral spin S=1/2 fermionic spinons, and states with spinless fermionic charge carriers. We illustrate these ideas on the honeycomb lattice, with field theories of such states and their phase transitions.
The anyonic excitations of a spin-liquid can feature fractional quantum numbers under space-group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice chiral spin liquid. We provide a method to detect these fractional quantum numbers in…
The unconventional low-lying spin excitations, recently observed in neutron scattering experiments on ${\rm Cs_2 Cu Cl_4}$, are explained with a spin liquid wave function. The dispersion relation as well as the wave vector of the incommensurate spin correlations are well reproduced within a projected BCS wave function with gapless and fractionalized spin-1/2 excitations around the nodes of the BCS gap function. The proposed wave function is shown to be very accurate for one-dimensional spin-1/2 systems, and remains similarly accurate in the two-dimensional model corresponding to ${\rm Cs_2 Cu …
We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and…
We investigate the real-time spin response of the $S=1$ Kitaev model upon stimuli of a pulsed magnetic field in one of the edges using the exact diagonalization method. It is found that the pulsed magnetic field has no effect on the appearance of the spin moments in the quantum spin liquid region, but induces the spin oscillations in the other edge region with a small magnetic field. This is understood by the existence of the itinerant quasiparticles, which carry the spin excitations without the spin polarization in the quantum spin liquid state. This suggests that the spin fractionalizations …
The sliding Luttinger liquids (LL) approach is applied to study fractional topological insulators (FTI). We show that FTI is the low energy fixed point of the theory for realistic spin-orbit and electron-electron interaction. We find that the topological phase pertains in the presence of interaction that breaks the spin invariance and its boundaries are even extended by those terms. Finally we show that one dimensional chiral anomaly in the LL leads to the emergence of topological Chern-Simons terms in the effective gauge theory of the FTI state.
The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they instead represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we show that the state characterized by such fractional oscillations still bears the signatures of spin momentum locking. Finally, we compare the spin-s…
Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the h…
The Kondo-Heisenberg model is used for a microscopic demonstration of existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. I use a non-perturbative approach where the strongest interactions are taken into account by means of exact solution, and corrections are controllable. In agreement with the general requirements formulated in (T. Senthil {\it et.al.} Phys. Rev. Lett. {\bf 90}, 216403 (2003)), the resulting metallic state represents a fractionalized Fermi liquid where well defined quasipar…
Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations. Several quasi-two dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacking. In this paper, we show that the inter-plane thermal conductivity in layered QSLs carries a unique signature of fractionalization. We examine several types of gapless QSL phases - a $Z_2$ QSL with either a Dirac spectrum or a spinon Fermi surface, and a $U(1)$ QSL with a Fermi surface. In all cases, the in-plane and $c-$axis thermal conductiviti…
Long-range entanglement in quantum spin liquids (QSLs) lead to novel low energy excitations with fractionalised quantum numbers and (in 2D) statistics. Experimental detection and manipulation of these excitations present a challenge particularly in view of diverse candidate magnets. A promising probe of fractionalisation is their coupling to phonons. Here we present Raman scattering results for the S = 1/2 honeycomb iridate Cu2IrO3, a candidate Kitaev QSL with fractionalised Majorana fermions and Ising flux excitations. We observe anomalous low temperature frequency shift and linewidth broaden…
Several heavy-fermion metals display a quantum phase transition from an antiferromagnetic metal to a heavy Fermi liquid. In some materials, however, recent experiments seem to find that the heavy Fermi liquid phase can be directly tuned into a non-Fermi liquid phase without apparent magnetic order. We analyze a candidate state for this scenario where the local moment system forms a spin liquid with gapless fermionic excitations. We discuss the thermal conductivity and spin susceptibility of this fractionalized state both in two and, in particular, three spatial dimensions for different tempera…
We present the theory of dynamical spin-response for the Kitaev honeycomb model, obtaining exact results for the structure factor (SF) in gapped and gapless, Abelian and non-Abelian quantum spin-liquid (QSL) phases. We also describe the advances in methodology necessary to compute these results. The structure factor shows signatures of spin-fractionalization into emergent quasiparticles -- Majorana fermions and fluxes of $Z_2$ gauge field. In addition to a broad continuum from spin-fractionalization, we find sharp ($δ$-function) features in the response. These arise in two distinct ways: from …
We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors $f=1/2$ and $f=1$ in the lowest Landau level. We use the evolution of ground-state entanglement entropy, fidelity susceptibility, and Hall conductance with increasing disorder strength to identify the underlying phase transitions. The critical disorder strengths obtained from these different quantities are consistent with each other, validating the reliability of our numerical calculations based on exact diagonalization. At $f=1/2$, we observe a clear transition from the bosonic L…
In this paper, we present a description of Haldane's Luttinger liquid which parallels Laughlin's theory of the Fractional Quantum Hall (FQH) incompressible fluid, both exhibiting similar ground states as well as fractional excitations. These two non-Fermi liquids are instances of a generic structure for low-dimensional quantum liquids which we propose to dub Jastrow-Luttinger Fractional Liquids. An important feature of such liquids is the complete fractionalization of the parent particle. In particular, in both one and two dimensions spin-charge separation can be achieved and is indeed suggest…
The fractionalization of elementary excitations in quantum spin systems is a central theme in current condensed matter physics. The Kitaev honeycomb spin model provides a prominent example of exotic fractionalized quasiparticles, composed of itinerant Majorana fermions and gapped gauge fluxes. However, identification of the Majorana fermions in a three-dimensional honeycomb lattice remains elusive. Here we report spectroscopic signatures of fractional excitations in the harmonic-honeycomb iridates $β$- and $γ$-Li$_2$IrO$_3$. Using polarization resolved Raman spectroscopy, we find that the dyna…
The emergence of fractionalized quasiparticles in quantum spin liquids has served a wealth of unconventional phenomena in frustrated magnets. In our work, we explore the various domain patterns of such fractionalized quasiparticles, especially focusing on charge defects in U(1) quantum spin liquids. We claim that emergent long range interaction between charge defects leads to characteristic structures with distinct length scales, where they can be controlled via the ratio of interaction strengths. In this context, the spin ice phase is the dilute gas of weakly interacting charges, whereas, the…
The nontrivialness of quantum spin liquid (QSL) typically manifests in the non-local observables that signifies their existence, however, this fact actually casts shadow on detecting QSL with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating dynamical signature of anyonic excitations and symmetry fractionalization in QSL. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that across the phase transitions from Z2 QSLs to different symmetry br…
We study one dimensional wires with spin-orbit coupling. We show that in the presence of Zeeman field and strong electron-electron interaction a clean wire may form fractional helical liquid states with phenomenology similar to fractional quantum Hall liquids. Most notably, the wire's two terminal conductance is predicted to show fractional quantized conductance plateaus at low electron density. When the system is proximity-coupled to a superconductor, fractional Majorana bound states may be stabilized. We discuss how disorder destabilizes these fractional phases. Possible experimental realiza…
One of the most successful theories of a non-Fermi liquid metallic state is the composite Fermi liquid (CFL) theory of the half-filled Landau level. In this paper, we study continuous quantum phase transitions out of the CFL state and into a Landau Fermi liquid, in the limit of no disorder and fixed particle number. This transition can be induced by tuning the bandwidth of the Landau level relative to the interaction energy, for instance through an externally applied periodic potential. We find a transition to the Landau Fermi liquid through a gapless Mott insulator with a Fermi surface of neu…
The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it ha…
Quantum spin liquids (QSLs) are exotic states of matter characterized by emergent gauge structures and fractionalized elementary excitations. The recently discovered triangular lattice antiferromagnet YbMgGaO$_4$ is a promising QSL candidate, and the nature of its ground state is still under debate. Here, we use neutron scattering to study the spin excitations in YbMgGaO$_4$ under various magnetic fields. Our data reveal a dispersive spin excitation continuum with clear upper and lower excitation edges under a weak magnetic field ($H=2.5$ T). Moreover, a spectral crossing emerges at the $Γ$ po…
Based on large-scale quantum Monte Carlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice quantum spin-$1/2$ model, which is known to harbor an extended $Z_2$ quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit-cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the $Z_2$ quantum spin l…
Fractionalized Fermi liquids (FL$^\ast$) have been introduced as non-Fermi-liquid metallic phases, characterized by coexisting electron-like charge carriers and local moments which itself form a fractionalized spin liquid. Here we investigate a Kondo lattice model on the honeycomb lattice with compass interactions among the local moments, a concrete model hosting FL$^\ast$ phases based on Kitaev's $\mathbb{Z}_2$ spin liquid. We characterize the FL$^\ast$ phases via perturbation theory, and we employ a Majorana-fermion mean-field theory to map out the full phase diagram. Most remarkably we find…
The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we uncover this effect in $α$-RuCl3 using inelastic X-ray scattering with meV resolut…
For the numerical simulation of the fractional quantum Hall effects on a finite disk, the rotational symmetry is the only symmetry that were used in diagonalizing the Hamiltonian. In this work, we propose a method of using the weak translational symmetry for the center of mass of the many-body system. With this approach, the bulk properties , such as the energy gap and the magneto-roton excitation are exactly consistent with that in the closed manifold like sphere and torus. As an application, we consider the FQH phase and its phase transition in the fast rotated dipolar fermions. We thus weap…
We consider Dirac electrons on the honeycomb lattice Kondo coupled to spin-1/2 degrees of freedom on the kagome lattice. The interactions between the spins are chosen along the lines of the Balents-Fisher-Girvin model that is known to host a $\mathbb{Z}_2$ spin liquid and a ferromagnetic phase. The model is amenable to sign free auxiliary field quantum Monte Carlo simulations. While in the ferromagnetic phase the Dirac electrons acquire a gap, they remain massless in the $\mathbb{Z}_2$ spin liquid phase due to the breakdown of Kondo screening. Since our model has an odd number of spins per uni…
Deconfined quantum critical points govern continuous quantum phase transitions at which fractionalized (deconfined) degrees of freedom emerge. Here we study dynamical signatures of the fractionalized excitations in a quantum magnet (the easy-plane J-Q model) that realize a deconfined quantum critical point with emergent O(4) symmetry. By means of large-scale quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation functions, we obtain the dynamic spin structure factors in the $S^{x}$ and $S^{z}$ channels. In both channels, we observe broad continua tha…
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.
An analytical solution of the Mott transition is obtained for the Hubbard model on the Bethe lattice in the large coordination number ($z$) limit. The excitonic binding of doublons (doubly occupied sites) and holons (empty sites) is shown to be the origin of a continuous Mott transition between a metal and an emergent quantum spin liquid insulator. The doublon-holon binding theory enables a different large-$z$ limit and a different phase structure than the dynamical meanfield theory by allowing intersite spinon correlations to lift the $2^N$-fold degeneracy of the local moments in the insulati…
Topologically ordered states of matter are generically characterized by excitations with quantum number fractionalization. A prime example is the spin liquid realized in Kitaev's honeycomb-lattice compass model where spin-flip excitations fractionalize into Majorana fermions and Ising gauge fluxes. While numerous compounds have been proposed to be proximate to such a spin-liquid phase, clear-cut evidence for fractionalized excitations is lacking. Here we employ microwave absorption measurements to study the low-energy excitations in $α$-RuCl$_3$ over a wide range of frequencies, magnetic field…
The Luttinger model of the one-dimensional Fermi gas is the cornerstone of modern understanding of interacting electrons in one dimension. In fact, the enormous class of systems whose universal behavior is adiabatically connected to it are now deemed Luttinger liquids. Recently, it has been shown that metallic single-walled carbon nanotubes are almost perfectly described by the Luttinger Hamiltonian. Indeed, strongly non-Fermi liquid behavior has been observed in a variety of DC transport experiments, in very good agreement with theoretical predictions. Here, we describe how fractional quasipa…
We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an internal metric, and show up as resonance peaks in the systems response to what is the fractional Hall analog of gravitational waves. Relation with existing and possible future experimental work that can detect these fractional quantum Hall gravitons and reveal their chirality are discussed.
The interplay of symmetry and topological order leads to a variety of distinct phases of matter, the Symmetry Enriched Topological (SET) phases. Here we discuss physical observables that distinguish different SETs in the context of Z$_2$ quantum spin liquids with SU(2) spin rotation invariance. We focus on the cylinder geometry, and show that ground state quantum numbers for different topological sectors are robust invariants which can be used to identify the SET phase. More generally these invariants are related to 1D symmetry protected topological phases when viewing the cylinder geometry as…
For topologically nontrivial and very narrow bands, Coulomb repulsion between electrons has been predicted to give rise to a spontaneous fractional quantum-Hall (FQH) state in absence of magnetic fields. Here we show that strongly correlated electrons in a t_2g-orbital system on a triangular lattice self-organize into a spin-chiral magnetic ordering pattern that induces precisely the required topologically nontrivial and flat bands. This behavior is very robust and does not rely on fine tuning. In order to go beyond mean field and to study the impact of longer-range interactions, we map the lo…
We employ a variational Monte Carlo approach to efficiently obtain the dynamical structure factor for the spin-1/2 $J_1-J_2$ Heisenberg model on the square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground state undergoes a continuous transition from a Néel antiferromagnet to a $\mathbb{Z}_{2}$ gapless spin liquid. We identify the characteristic spectral features in both phases and highlight the existence of a broad continuum of excitations in the proximity of the spin-liquid phase. The magnon branch, which dominates the spectrum of the unfrustrated Heisenberg model, gradual…
We show that there is a close correspondence between the physical properties of holographic metals near charged black holes in anti-de Sitter (AdS) space, and the fractionalized Fermi liquid phase of the lattice Anderson model. The latter phase has a "small" Fermi surface of conduction electrons, along with a spin liquid of local moments. This correspondence implies that certain mean-field gapless spin liquids are states of matter at non-zero density realizing the near-horizon, AdS_2 x R^2 physics of Reissner-Nordstrom black holes.
Charge fractionalization is the phenomenon where quasi-particle excitations in a many-particle system appear with non-integer values relative to the fundamental charge unit. Examples of such systems are known from field theoretical models and from physical realizations. Recently there has been an interest in charge fractionalization in one-dimensional systems described by Luttinger liquid theory. These are gapless systems and that gives rise to the question whether non-integer charges should be regarded as sharp in the same meaning as in a gapped system. In this talk I first give an introducti…
Helical Luttinger liquids, appearing at the edge of two-dimensional topological insulators, represent a new paradigm of one-dimensional systems, where peculiar quantum phenomena can be investigated. Motivated by recent experiments on charge fractionalization, we propose a setup based on helical Luttinger liquids that allows to time-resolve, in addition to charge fractionalization, also spin-charge separation and pure spin fractionalization. This is due to the combined presence of spin-momentum locking and interactions. We show that electric time-resolved measurements can reveal both charge and…
We study fractionalization in a spin-liquid Mott insulator defined by a Gutzwiller projected BCS state |0> at half-filling. We construct a trial vison (Z2 vortex) state |V> by projecting an hc/2e vortex and determine when it is orthogonal to |0>. Using a combination of analytical arguments and Monte Carlo calculations we show that generically the spin-liquid is Z2 fractionalized. For microscopic parameters appropriate for high Tc cuprates, we estimate that the vison gap Ev << J, consistent with recent experimental bounds, due to proximity to the bipartite symmetric point where Ev = 0.
