We study quantum phase transitions involving fractional quantum Hall states, using numerical calculations of entanglements and related quantities. We tune finite-size wavefunctions on spherical geometries, by varying the interaction potential away from the Coulomb interaction. We uncover signatures of quantum phase transitions contained in the scaling behavior of the entropy of entanglement between two parts of the sphere. In addition to the entanglement entropy, we show that signatures of quantum phase transitions also appear in other aspects of the reduced density matrix of one part of the sphere.
We show that the entanglement spectrum associated with a certain class of strongly correlated many-body states --- the wave functions proposed by Laughlin and Jain to describe the fractional quantum Hall effect --- can be very well described in terms of a simple model of non-interacting (or weakly interacting) composite fermions.
We discuss charged topological spin textures in quantum Hall ferromagnets in which the electrons carry a pseudospin as well as the usual spin degree of freedom, as is the case in bilayer GaAs or monolayer graphene samples. We develop a theory which treats spin and pseudospin on a manifestly equal footing, which may also be of help in visualizing the relevant spin textures. We in particular consider the entanglement of spin and pseudospin in the presence of realistic anisotropies. An entanglement operator is introduced which generates families of degenerate Skyrmions with differing entanglement…
We use particle entanglement spectra to characterize bosonic quantum Hall states on lattices, motivated by recent studies of bosonic atoms on optical lattices. Unlike for the related problem of fractional Chern insulators, very good trial wavefunctions are known for fractional quantum Hall states on lattices. We focus on the entanglement spectra for the Laughlin state at $ν=1/2$ for the non-Abelian Moore-Read state at $ν=1$. We undertake a comparative study of these trial states to the corresponding groundstates of repulsive two-body or three-body contact interactions on the lattice. The magni…
The entanglement entropy of the $ν= 1/3$ and $ν= 5/2$ quantum Hall states in the presence of short range random disorder has been calculated by direct diagonalization. A microscopic model of electron-electron interaction is used, electrons are confined to a single Landau level and interact with long range Coulomb interaction. For very weak disorder, the values of the topological entanglement entropy are roughly consistent with expected theoretical results. By considering a broader range of disorder strengths, the fluctuation in the entanglement entropy was studied in an effort to detect quantu…
Magnetic hopfions are topologically protected three-dimensional solitons that are constituted by a tube which exhibits a topologically nontrivial spin texture in the cross-section profile and is closed to a torus. Here we show that the hopfion's locally uncompensated emergent field leads to a topological Hall signature, although the topological Hall effect vanishes on the global level. The topological Hall signature is switchable by magnetic fields or electric currents and occurs independently of the anomalous and conventional Hall effects. It can therefore be exploited to electrically detect …
We study the entanglement production in a quantum spin Hall ring geometry where electrons of opposite spins are emitted in pairs from a source and collected in two different detectors. Postselection of coincidence detector events gives rise to entanglement in the system, measurable through correlations between the outcomes in the detectors. We have chosen a geometry such that the entanglement depends on the dynamical phases picked up by the edge states as they move around the ring. In turn, the dependence of the phases on gate potential and Rashba interaction allows for a precise electrical co…
We report distinct nonanalytic signatures in the spin-orbit entanglement of a 2D electron gas with Rashba interactions at integer values of the filling factor and at certain level crossings. The accompanying sharp changes in the bulk spin-orbit entanglement entropy can be probed by measuring the fluctuation in the transverse spin polarization of the electron gas.
We show that non-abelian quantum Hall states can be identified by experimental measurements of the temperature-dependence of either the electrochemical potential or the orbital magnetization. The predicted signals of non-abelian statistics are within experimental resolution, and can be clearly distinguished from other contributions under realistic circumstances. The proposed measurement technique also has the potential to resolve spin-ordering transitions in low density electronic systems in the Wigner crystal and strongly-interacting Luttinger liquid regimes.
The measurement of quantum entanglement in many-body systems remains challenging. One experimentally relevant fact about quantum entanglement is that in systems whose degrees of freedom map to free fermions with conserved total particle number, exact relations hold relating the Full Counting Statistics associated with the bipartite charge fluctuations and the sequence of R\' enyi entropies. We draw a correspondence between the bipartite charge fluctuations and the entanglement spectrum, mediated by the R\' enyi entropies. In the case of the integer quantum Hall effect, we show that it is possi…
In the presence of a scattering potential, electron transport in a quantum wire is known to be dramatically modified by backward scattering and unaffected by forward scattering processes. We show that the scenario is quite different in Quantum Spin Hall effect edge states coupled at a constriction. The helical nature of these states leads to the appearance of a forward scattering spin channel that is absent in other Luttinger liquid realizations. Suitably applied ac gate voltages can thus operate on the spin of electrons tunneling across the constriction, and induce in the dc tunneling current…
We use bosonic field theories and the infinite system density matrix renormalization group (iDMRG) method to study infinite strips of fractional quantum Hall (FQH) states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge mode exponents and momenta without finite-size errors. We analyze states in the first and second level of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid ($χ$LL) theory. The results confirm the universality of scaling exponents in chiral edges and demonstr…
We compute the entanglement entropy, in real space, of the ground state of the integer Quantum Hall states for three different domains embedded in the torus, the disk and the sphere. We establish the validity of the area law with a vanishing value of the topological entanglement entropy. The entropy per unit length of the perimeter depends on the filling fraction, but it is independent of the geometry.
We study the real-space entanglement spectrum for fractional quantum Hall systems, which maintains locality along the spatial cut, and provide evidence that it possesses a scaling property. We also consider the closely-related particle entanglement spectrum, and carry out the Schmidt decomposition of the Laughlin state analytically at large size.
The implementation of a functional quantum computer involves entangling and coherent manipulation of a large number of qubits. For qubits based on electron spins confined in quantum dots, which are among the most investigated solid-state qubits at present, architectural challenges are often encountered in the design of quantum circuits attempting to assemble the qubits within the very limited space available. Here, we provide a solution to such challenges based on an approach to realizing entanglement of spin qubits over long distances. We show that long-range Ruderman-Kittel-Kasuya-Yosida int…
We present a detailed analysis of bipartite entanglement entropies in fractional quantum Hall (FQH) states, considering both abelian (Laughlin) and non-abelian (Moore-Read) states. We derive upper bounds for the entanglement between two subsets of the particles making up the state. We also consider the entanglement between spatial regions supporting a FQH state. Using the latter, we show how the so-called topological entanglement entropy of a FQH state can be extracted from wavefunctions for a limited number of particles.
We analyze the entanglement spectrum of Laughlin states on the torus and show that it is arranged in towers, each of which is generated by modes of two spatially separated chiral edges. This structure is present for all torus circumferences, which allows for a microscopic identification of the prominent features of the spectrum by perturbing around the thin torus limit.
We study the entanglement properties of some fractional quantum Hall liquids. We calculate the entanglement of the Laughlin wave function and the wave functions that are generated by the K-matrix using the modified entanglement measure of indistinguishable fermions that is first proposed by Paškauskas and You[1].
The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitation shows a crossover from metallic behavior at short sample sizes to localized at longer length. The dependence of the crossover as function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many particle critical energy in the vicinity of the Fermi energy. Impl…
The statistics of tunneling current in a fractional quantum Hall sample with an antidot is studied in the chiral Luttinger liquid picture of edge states. A comparison between Fano factor and skewness is proposed in order to clearly distinguish the charge of the carriers in both the thermal and the shot limit. In addition, we address effects on current moments of non-universal exponents in single-quasiparticle propagators. Positive correlations, result of propagators behaviour, are obtained in the shot noise limit of the Fano factor, and possible experimental consequences are outlined.
We compute directly the entanglement entropy of spatial regions in Chern-Simons gauge theories in 2+1 dimensions using surgery. We use these results to determine the universal topological piece of the entanglement entropy for Abelian and non-Abelian quantum Hall fluids.
Generally speaking, the entanglement entropy (EE) between two subregions of a gapped quantum many-body state is proportional to the area/length of their interface due to the short range quantum correlation. However, the so-called area law is violated logarithmically in a quantum critical phase. Moreover, the subleading correction exists in a long range entangled topological phases. It is referred to as topological EE which is related to the quantum dimension of the collective excitation in the bulk. Further more, if a non-smooth sharp angle is in the presence of the subsystem boundary, a unive…
Hall viscosity is a non-dissipative response function describing momentum transport in two-dimensional systems with broken parity. It is quantized in the quantum Hall regime, and contains information about the topological order of the quantum Hall state. Hall viscosity can distinguish different quantum Hall states with identical Hall conductances, but different topological order. To date, an experimentally accessible signature of Hall viscosity is lacking. We exploit the fact that Hall viscosity contributes to charge transport at finite wavelengths, and can therefore be extracted from non-loca…
We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wavefunction for the $ν$ = 5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the \textit{only} levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entangle…
We propose an entanglement detector composed of two quantum spin Hall insulators and a side gate deposited on one of the edge channels. For an ac gate voltage, the differential noise contributed from the entangled electron pairs exhibits the nontrivial step structures, from which the spin entanglement concurrence can be easily obtained. The possible spin dephasing effects in the quantum spin Hall insulators are also included.
We study the entanglement spectra of bilayer quantum Hall systems at total filling factor nu=1. In the interlayer-coherent phase at layer separations smaller than a critical value, the entanglement spectra show a striking similarity to the energy spectra of the corresponding monolayer systems around half filling. The transition to the incoherent phase can be followed in terms of low-lying entanglement levels. Finally, we describe the connection between those two types of spectra in terms of an effective temperature leading to relations for the entanglement entropy which are in full analogy to …
We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite cylinders, which provides an efficient way of calculating arbitrary observables. We extend this approach to the charged excitations and numerically compute their Berry phases. Finally, we present an algorithm for numerically computing the real-space entanglement spectrum starting from an arbitrary orbital basis MPS, which allows us to study the scaling proper…
We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for various ground and excited states, with or without mass anisotropy. We focus on an important class of regions that contain sharp corners or cusps, leading to a geometric angle-dependent contribution to the EE. We unravel surprising relations by comparing this corner term at different fillings. We further find that the corner term, when properly normalized, has …
Parity anomaly is a quantum mechanical effect that the parity symmetry in a two-dimensional classical action is failed to be restored in any regularization of the full quantum theory and is characterized by a half-quantized Hall conductivity. Here we propose a scheme to explore the experimental signature from parity anomaly in the measurement of optical Hall conductivity, in which the optical Hall conductivity is nearly half quantized for a proper range of frequency. The behaviors of optical Hall conductivity are studied for several models, which reveal the appearance of half-quantized Hall co…
We present a new approach to obtaining the scaling behavior of the entanglement entropy in fractional quantum Hall states from finite-size wavefunctions. By employing the torus geometry and the fact that the torus aspect ratio can be readily varied, we can extract the entanglement entropy of a spatial block as a continuous function of the block boundary. This approach allows us to extract the topological entanglement entropy with an accuracy superior to what is possible on the spherical or disc geometry, where no natural continuously variable parameter is available. Other than the topological …
We investigate the entanglement spectra arising from sharp real-space partitions of the system for quantum Hall states. These partitions differ from the previously utilized orbital and particle partitions and reveal complementary aspects of the physics of these topologically ordered systems. We show, by constructing one to one maps to the particle partition entanglement spectra, that the counting of the real-space entanglement spectra levels for different particle number sectors versus their angular momentum along the spatial partition boundary is equal to the counting of states for the system…
We present an interferometric scheme producing orbital entanglement in a quantum Hall system upon electron-hole pair emission via tunneling. The proposed setup is an electronic version of the optical interferometer proposed by Cabello et al. [Phys. Rev. Lett. 102, 040401 (2009)], and is feasible with present technology. It requires single-channel propagation and a single primary source. We discuss the creation of entanglement and its detection by the violation of a Bell inequality.
We demonstrate theoretically that the thermal Hall effect of magnons in collinear antiferromagnetic insulators is an indicator of magnetic and topological phase transitions in the magnon spectrum. The transversal heat current of magnons caused by a thermal gradient is calculated for an antiferromagnet on a honeycomb lattice. An applied magnetic field drives the system from the antiferromagnetic phase via a spin-flop phase into the field-polarized phase. Besides these magnetic phase transitions we find topological phase transitions within the spin-flop phase. Both types of transitions manifest …
Unconventional responses upon breaking discrete or crystal symmetries open avenues for exploring emergent physical systems and materials. By breaking inversion symmetry, a nonlinear Hall signal can be observed, even in the presence of time-reversal symmetry, quite different from the conventional Hall effects. Low-symmetry two-dimensional materials are promising candidates for the nonlinear Hall effect, but it is less known when a strong nonlinear Hall signal can be measured, in particular, its connections with the band-structure properties. By using model analysis, we find prominent nonlinear …
The critical theories for the topological phase transitions of integer quantum Hall states to a trivial insulating state with the same symmetry can be obtained by calculating the ground state entanglement spectrum under a symmetric checkerboard bipartition. In contrast to the gapless edge excitations under the left-right bipartition, a quantum network with bulk gapless excitations naturally emerges at the Brillouin zone center without fine tuning. On a large finite lattice, the resulting critical theory for the $ν=1$ state is the (2+1) dimensional relativistic quantum field theory characterize…
Signatures of the non-Abelian statistics of quasi-particles in the $ν=5/2$ quantum Hall state are predicted to be present in the current-voltage characteristics of tunneling through one or two quantum Hall puddles of Landau filling $ν_a$ embedded in a bulk of filling $ν_b$ with $(ν_a,ν_b)=(2,5/2)$ and $(ν_a,ν_b)=(5/2,2)$.
We demonstrate that entangled electron-hole pairs can be produced and detected in a quantum spin Hall insulator with a constriction that allows for a weak inter-edge tunneling. A violation of a Bell inequality, which can be constructed in terms of low-frequency nonlocal current-current correlations, serves as a detection of the entanglement. We show that the maximum violation of a Bell inequality can be naturally achieved in this setup, without a need to fine tune tunneling parameters. This may provide a viable route to producing spin entanglement in the absence of any correlations and pairing…
The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry information about topologic order in the ground state, was extracted for filling factors 1/3, 1/5 and 5/2. The results for 1/3 and 1/5 are consistent with the topological entanglement entropy for the Laughlin wave function. The 5/2 state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.
We show the low-lying excitations at filling factor $ν=n+1/3$ with realistic interactions are contained completely within the well-defined Hilbert space of "Gaffnian quasiholes". Each Laughlin quasihole can thus be understood as a bound state of two Gaffnian quasiholes, which in the lowest Landau level (LLL) behaves like "partons" with "asymptotic freedom" mediated by neutral excitations acting as "gluons". Near the experimentally observed nematic FQH phase in higher LLs, quasiholes become weakly bounded and fractionalise with rich dynamical properties. By studying the effective interactions b…
We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that form in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system's signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that form between Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.
In time-reversal invariant systems, all charge Hall effects predicted so far are extrinsic effects due to the dependence on the relaxation time. We explore intrinsic Hall signatures by studying quantum noise spectrum of the Hall current in time-reversal invariant systems, and discover intrinsic thermal Hall noises in both linear and nonlinear regimes. As the band geometric characteristics, quantum geometric tensor and Berry curvature play critical roles in various Hall effects, so are their quantum fluctuations. It is found that the thermal Hall noise in linear order of the electric field is p…
The lateral photovoltage generated in the plane of a two-dimensional electron system (2DES) by a focused light spot, exhibits a fine-structure in the quantum oscillations in a magnetic field near the Quantum Hall conductivity minima. A double peak structure occurs near the minima of the longitudinal conductivity oscillations. This is the characteristic signature of the interplay between screening and Landau quantization.
The activation gap Delta of the fractional quantum Hall state at constant filling n =1/3 is measured in wide range of perpendicular magnetic field B. Despite the full spin polarization of the incompressible ground state, we observe a sharp crossover between a low-field linear dependence of Delta on B associated to spin texture excitations and a Coulomb-like behavior at large B. From the global gap-reduction we get information about the mobility edges in the fractional quantum Hall regime.
We identify an optical signature for detecting entanglement in experimental nanostructure systems comprising coupled excitonic qubits. This signature owes its strength to non-Markovian dynamical effects in the second-order temporal coherence function of the emitted radiation. We calculate autocorrelation and cross-correlation functions for both selective and collective light excitation, and prove that the coherence properties of the emitted light do indeed carry information about the entanglement of the initial multi-qubit state. We also show that this signature can survive in the presence of …
Of the available classes of insulators which have been shown to contain topologically non-trivial properties one of the most important is class AII, which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$ This class has been the subject of significant attention as it encompasses non-trivial Z$_2$ topological insulators such as the quantum spin Hall (QSH) state and the 3D strong topological insulator. One of the defining properties of this system is the robustness of the state under the addition of disorder that preserves $T.$ In this letter, we explore the phase diagram o…
Motivated by the recent Coulomb drag experiment of M. P. Lilly et. al, we study the Coulomb drag in a two-layer system with Landau level filling factor $ν=1/2$. We find that the drag conductivity in the incompressible paired quantum Hall state at zero temperature can be finite. The drag conductivity is also greatly enhanced above $T_c$, at which the transition between the weakly coupled compressible liquids and the paired quantum Hall liquid takes place. We discuss the implications of our results for the recent experiment.
Motivated by the recent surge of field-driven phenomena discussed for Kitaev materials, in particular the experimental observation of a finite thermal Hall effect and theoretical proposals for the emergence of additional spin liquid phases beyond the conventional Kitaev spin liquid, we develop a theoretical understanding of the thermal Hall effect in honeycomb Kitaev materials in magnetic fields. Our focus is on gapless U(1) spin liquids with a spinon Fermi surface, which have been shown to arise as field-induced phases. We demonstrate that in the presence of symmetry-allowed, second-neighbor …
The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a ``bunching'' effect, whi…
We consider integer quantum Hall states and calculate bulk entanglement spectrum by formulating the correlation matrix in guiding center representation. Our analytical approach is based on the projection operator with redefining the inner product of states in Hilbert space to take care of the restriction imposed by the (rectangle-tiled) checkerboard partition. The resultant correlation matrix contains the coupling constants between states of different guiding centers parameterized by magnetic length and the period of partition. We find various band-crossings by tuning the flux $Φ$ threading ea…
Coulomb diamonds are the archetypal signatures of Coulomb blockade, a well-known charging effect mainly observed in nanometer-sized "electronic islands" tunnel-coupled with charge reservoirs. Here, we identify apparent Coulomb diamond features in the scanning gate spectroscopy of a quantum point contact carved out of a semiconductor heterostructure, in the quantum Hall regime. Varying the scanning gate parameters and the magnetic field, the diamonds are found to smoothly evolve to checkerboard patterns. To explain this surprising behavior, we put forward a model which relies on the presence of…
We investigate the effect of interactions on shot noise in $ν=2$ quantum Hall edges, where a repulsive coupling between co-propagating edge modes is expected to give rise to charge fractionalization. Using the method of non-equilibrium bosonization, we find that even asymptotically the edge distribution function depends in a sensitive way on the interaction strength between the edge modes. We compute shot noise and Fano factor from the asymptotic distribution function, and from comparison with a reference model of fractionalized excitations we find that the Fano factor can be close to the valu…
We study a two-dimensional electron system in the presence of spin-orbit interaction. It is shown analytically that the spin-orbit interaction acts as a transversal effective electric field, whose orientation depends on the sign of the $\hat{z}$-axis spin projection. This effect doesn't require any driving external field and is inherent to the spin-orbit interactions present in semiconductor materials. Therefore, it should manifest in both closed and open systems. It is proposed an experiment to observe the intrinsic spin Hall effect in the far infrared absorption of an asymmetric semiconducto…
Boundaries constitute a rich playground for quantum many-body systems because they can lead to novel degrees of freedom such as protected boundary states in topological phases. Here, we study the groundstate of integer quantum Hall systems in the presence of boundaries through the reduced density matrix of a spatial region. We work in the lowest Landau level and choose our region to intersect the boundary at arbitrary angles. The entanglement entropy (EE) contains a logarithmic contribution coming from the chiral edge modes, and matches the corresponding conformal field theory prediction. We u…
We study coherence and entanglement properties of the state space of a composite bi-fermion (two electrons pierced by $λ$ magnetic flux lines) at one Landau site of a bilayer quantum Hall system. In particular, interlayer imbalance and entanglement (and its fluctuations) are analyzed for a set of $U(4)$ coherent (\emph{quasiclassical}) states generalizing the standard pseudospin $U(2)$ coherent states for the spin-frozen case. The interplay between spin and pseudospin degrees of freedom opens new possibilities with regard to the spin-frozen case. Actually, spin degrees of freedom make interlay…
Constrictions in fractional quantum Hall (FQH) systems not only facilitate backscattering between counter-propagating edge modes, but also may reduce the constriction filling fraction $ν_c$ with respect to the bulk filling fraction $ν_b$. If both $ν_b$ and $ν_c$ correspond to incompressible FQH states, at least part of the constriction region is surrounded by composite edges, whose low energy dynamics is characterized by a charge mode and one or several neutral modes. In the incoherent regime, decay of neutral modes describes the equilibration of composite FQH edges, while in the limit of cohe…
