arXiv subjects

Nicolas Regnault

Publications and source records attributed to Nicolas Regnault.

At least 127 records · Page 7Linked to original sources

arXiv2017

Entanglement of Exact Excited Eigenstates of the Hubbard Model in Arbitrary Dimension

We compute exactly the von Neumann entanglement entropy of the eta-pairing states - a large set of exact excited eigenstates of the Hubbard Hamiltonian. For the singlet eta-pairing states the entropy scales with the logarithm of the spatial dimension of the (smaller) partition. For the eta-pairing states with finite spin magnetization density, the leading term can scale as the volume or as the area-times-log, depending on the momentum space occupation of the Fermions with flipped spins. We also compute the corrections to the leading scaling. In order to study the eigenstate thermalization hypothesis (ETH), we also compute the entanglement Renyi entropies of such states and compare them with the corresponding entropies of thermal density matrix in various ensembles. Such states, which we find violate strong ETH, may provide a useful platform for a detailed study of the time-dependence of the onset of thermalization due to perturbations which violate the total pseudospin conservation.

cond-mat.str-el↗

arXiv2017

A simple anisotropic three-dimensional quantum spin liquid with fracton topological order

We present a three-dimensional cubic lattice spin model, anisotropic in the $\hat{z}$ direction, that exhibits fracton topological order. The latter is a novel type of topological order characterized by the presence of immobile pointlike excitations, named fractons, residing at the corners of an operator with two-dimensional support. As other recent fracton models, ours exhibits a subextensive ground state degeneracy: On an $L_x\times L_y\times L_z$ three-torus, it has a $2^{2L_z}$ topological degeneracy, and an additional non-topological degeneracy equal to $2^{L_xL_y-2}$. The fractons can be combined into composite excitations that move either in a straight line along the $\hat{z}$ direction, or freely in the $xy$ plane at a given height $z$. While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system. We find zero energy modes on the surfaces perpendicular to either the $\hat{x}$ or $\hat{y}$ directions, and their absence on the surfaces normal to $\hat{z}$. This result can be explained using the properties of the two kinds of composite two-fracton mobile excitations.

cond-mat.str-el↗

arXiv2017

Probing many-body localization with neural networks

We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.

cond-mat.dis-nn↗

arXiv2017

Characterizing the many-body localization transition through the entanglement spectrum

We numerically explore the many body localization (MBL) transition through the lens of the {\it entanglement spectrum}. While a direct transition from localization to thermalization is believed to obtain in the thermodynamic limit (the exact details of which remain an open problem), in finite system sizes there exists an intermediate `quantum critical' regime. Previous numerical investigations have explored the crossover from thermalization to criticality, and have used this to place a numerical {\it lower} bound on the critical disorder strength for MBL. A careful analysis of the {\it high energy} part of the entanglement spectrum (which contains universal information about the critical point) allows us to make the first ever observation in exact numerics of the crossover from criticality to MBL and hence to place a numerical {\it upper bound} on the critical disorder strength for MBL.

cond-mat.dis-nn↗

arXiv2017

Emergent particle-hole symmetry in spinful bosonic quantum Hall systems

When a fermionic quantum Hall system is projected into the lowest Landau level, there is an exact particle-hole symmetry between filling fractions $ν$ and $1-ν$. We investigate whether a similar symmetry can emerge in bosonic quantum Hall states, where it would connect states at filling fractions $ν$ and $2-ν$. We begin by showing that the particle-hole conjugate to a composite fermion `Jain state' is another Jain state, obtained by reverse flux attachment. We show how information such as the shift and the edge theory can be obtained for states which are particle-hole conjugates. Using the techniques of exact diagonalization and infinite density matrix renormalization group, we study a system of two-component (i.e., spinful) bosons, interacting via a $δ$-function potential. We first obtain real-space entanglement spectra for the bosonic integer quantum Hall effect at $ν=2$, which plays the role of a filled Landau level for the bosonic system. We then show that at $ν=4/3$ the system is described by a Jain state which is the particle-hole conjugate of the Halperin (221) state at $ν=2/3$. We show a similar relationship between non-singlet states at $ν=1/2$ and $ν=3/2$. We also study the case of $ν=1$, providing unambiguous evidence that the ground state is a composite Fermi liquid. Taken together our results demonstrate that there is indeed an emergent particle-hole symmetry in bosonic quantum Hall systems.

cond-mat.str-el↗

arXiv2017

The SkyMapper Transient Survey

The SkyMapper 1.3 m telescope at Siding Spring Observatory has now begun regular operations. Alongside the Southern Sky Survey, a comprehensive digital survey of the entire southern sky, SkyMapper will carry out a search for supernovae and other transients. The search strategy, covering a total footprint area of ~2000 deg2 with a cadence of $\leq 5$ days, is optimised for discovery and follow-up of low-redshift type Ia supernovae to constrain cosmic expansion and peculiar velocities. We describe the search operations and infrastructure, including a parallelised software pipeline to discover variable objects in difference imaging; simulations of the performance of the survey over its lifetime; public access to discovered transients; and some first results from the Science Verification data.

astro-ph.IM↗

arXiv2016

Many body localization and thermalization: insights from the entanglement spectrum

We study the entanglement spectrum in the many body localizing and thermalizing phases of one and two dimensional Hamiltonian systems, and periodically driven `Floquet' systems. We focus on the level statistics of the entanglement spectrum as obtained through numerical diagonalization, finding structure beyond that revealed by more limited measures such as entanglement entropy. In the thermalizing phase the entanglement spectrum obeys level statistics governed by an appropriate random matrix ensemble. For Hamiltonian systems this can be viewed as evidence in favor of a strong version of the eigenstate thermalization hypothesis (ETH). Similar results are also obtained for Floquet systems, where they constitute a result `beyond ETH', and show that the corrections to ETH governing the Floquet entanglement spectrum have statistical properties governed by a random matrix ensemble. The particular random matrix ensemble governing the Floquet entanglement spectrum depends on the symmetries of the Floquet drive, and therefore can depend on the choice of origin of time. In the many body localized phase the entanglement spectrum is also found to show level repulsion, following a semi-Poisson distribution (in contrast to the energy spectrum, which follows a Poisson distribution). This semi-Poisson distribution is found to come mainly from states at high entanglement energies. The observed level repulsion only occurs for interacting localized phases. We also demonstrate that equivalent results can be obtained by calculating with a single typical eigenstate, or by averaging over a microcanonical energy window - a surprising result in the localized phase. This discovery of new structure in the pattern of entanglement of localized and thermalizing phases may open up new lines of attack on many body localization, thermalization, and the localization transition.

cond-mat.stat-mech↗

arXiv2016

Rapidly Rising Transients in the Supernova - Superluminous Supernova Gap

We present observations of four rapidly rising (t_{rise}~10d) transients with peak luminosities between those of supernovae (SNe) and superluminous SNe (M_{peak}~-20) - one discovered and followed by the Palomar Transient Factory (PTF) and three by the Supernova Legacy Survey (SNLS). The light curves resemble those of SN 2011kl, recently shown to be associated with an ultra-long-duration gamma ray burst (GRB), though no GRB was seen to accompany our SNe. The rapid rise to a luminous peak places these events in a unique part of SN phase space, challenging standard SN emission mechanisms. Spectra of the PTF event formally classify it as a Type II SN due to broad Halpha emission, but an unusual absorption feature, which can be interpreted as either high velocity Halpha (though deeper than in previously known cases) or Si II (as seen in Type Ia SNe), is also observed. We find that existing models of white dwarf detonations, CSM interaction, shock breakout in a wind (or steeper CSM) and magnetar spindown can not readily explain the observations. We consider the possibility that a "Type 1.5 SN" scenario could be the origin of our events. More detailed models for these kinds of transients and more constraining observations of future such events should help better determine their nature.

astro-ph.CO↗

arXiv2015

Universal entanglement spectra in critical spin chains

We advocate that in critical spin chains, and possibly in a larger class of 1D critical models, a gap in the momentum-space entanglement spectrum separates the universal part of the spectrum, which is determined by the associated conformal field theory, from the non-universal part, which is specific to the model. To this end, we provide affirmative evidence from multicritical spin chains with low energy sectors described by the SU(2)$_2$ or the SU(3)$_1$ Wess-Zumino-Witten model.

cond-mat.str-el↗

arXiv2015

Phase diagram of $ν=\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings

We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor $ν=1$ in the lowest Landau level. We consider short-range interactions within and between the two layers, as well as the inter-layer tunneling. In the fully polarized regime, we provide an updated detailed numerical analysis to establish the presence of the Moore-Read phase of both even and odd numbers of particles. In the actual bilayer situation, we find that both inter-layer interactions and tunneling can provide the physical mechanism necessary for the low-energy physics to be driven by the fully polarized regime, thus leading to the emergence of the Moore-Read phase. Inter-layer interactions favor a ferromagnetic phase when the system is $SU(2)$ symmetric, while the inter-layer tunneling acts as a Zeeman field polarizing the system. Besides the Moore-Read phase, the $(220)$ Halperin state and the coupled Moore-Read state are also realized in this model. We study their stability against each other.

cond-mat.str-el↗

arXiv2015

Triplet FFLO Superconductivity in the doped Kitaev-Heisenberg Honeycomb Model

We provide analytical and numerical evidence of a spin-triplet FFLO superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of 6 inversion symmetry centers for the Fermi surface at non zero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these non-trivial momenta, causing the spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion analysis, we find that the superconductivity has three separated degenerate ground states with three different spin-triplet pairings. This picture is also supported by exact diagonalizations on finite clusters.

cond-mat.str-el↗

arXiv2015

Projective construction of the $\mathbb{Z}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the $\mathbb{Z}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of $\mathbb{Z}_k$ ground states on the torus. We develop an alternative projective construction of $\mathbb{Z}_k$ Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.

cond-mat.str-el↗

arXiv2015

Characterization of quasiholes in fractional Chern insulators

We provide a detailed study of the Abelian quasiholes of $ν=1/2$ bosonic fractional quantum Hall states on the torus geometry and in fractional Chern insulators. We find that the density distribution of a quasihole in a fractional Chern insulator can be related to that of the corresponding fractional quantum Hall state by choosing an appropriate length unit on the lattice. This length unit only depends on the lattice model that hosts the fractional Chern insulator. Therefore, the quasihole size in a fractional Chern insulator can be predicted for any lattice model once the quasihole size of the corresponding fractional quantum Hall state is known. We discuss the effect of the lattice embedding on the quasihole size. We also perform the braiding of quasiholes for fractional Chern insulator models to probe the fractional statistics of these excitations. The numerical values of the braiding phases accurately match the theoretical predictions.

cond-mat.str-el↗

arXiv2014

Fluctuations and Entanglement spectrum in quantum Hall states

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 possible to reproduce the generic features of the entanglement spectrum from a measurement of the second charge cumulant only. Additionally, asking whether it is possible to extend the free fermion result to the $ν=1/3$ fractional quantum Hall case, we provide numerical evidence that the answer is negative in general. We further address the problem of quantum Hall edge states described by a Luttinger liquid, and derive expressions for the spectral functions of the real space entanglement spectrum at a quantum point contact realized in a quantum Hall sample.

cond-mat.mes-hall↗

arXiv2013

Spin-singlet Gaffnian wave function for fractional quantum Hall systems

We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave functions, namely the non-Abelian spin-singlet state and the nonunitary Gaffnian wave function. This is a spin-singlet generalization of the spin-polarized Gaffnian, which we call the "spin-singlet Gaffnian" (SSG). In this paper we present evidence demonstrating that the SSG corresponds to the ground state of a certain local Hamiltonian, which we explicitly construct, and, further, we provide a relatively simple analytic expression for the unique ground-state wave functions, which we define as the zero energy eigenstates of that local Hamiltonian. In addition, we have determined a certain nonunitary, rational conformal field theory which provides an underlying description of the SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit. In order to verify our construction, we implement two recently proposed techniques for the analysis of fractional quantum Hall trial states: The "spin dressed squeezing algorithm", and the "generalized Pauli principle".

cond-mat.str-el↗

arXiv2012

Screening Behavior and Scaling Exponents from Quantum Hall Wavefunctions

We provide a robust and generic method to assess the screening properties and extract the scaling exponents of quasiparticle edge excitations of quantum Hall states from model wavefunctions. We numerically implement this method for the fundamental quasihole and hole excitations of several model states. For the Laughlin, Moore-Read, and Z_3-Read-Rezayi states, we find agreement with the predicted edge theory, verifying the bulk-edge correspondence. We also use this to obtain the first clear microscopic demonstration of the pathologies of the Gaffnian wavefunctions.

cond-mat.mes-hall↗

arXiv2011

From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions

We study the Haffnian and Haldane-Rezayi quantum Hall wave functions and their quasihole excitations by means of their `root configurations', and point out a close connection between these seemingly different states. For both states, we formulate a `generalized Pauli-principle', which allows to count the degeneracies of these states. The connection between these states might elucidate the underlying theory describing the `irrational' Haffnian state.

cond-mat.str-el↗

arXiv2010

Decomposition of fractional quantum Hall states: New symmetries and approximations

We provide a detailed description of a new symmetry structure of the monomial (Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall states first obtained in Ref. 1, which we now extend to spin-singlet states. We show that the Haldane-Rezayi spin-singlet state can be obtained without exact diagonalization through a differential equation method that we conjecture to be generic to other FQH model states. The symmetry rules in Ref. 1 as well as the ones we obtain for the spin singlet states allow us to build approximations of FQH states that exhibit increasing overlap with the exact state (as a function of system size). We show that these overlaps reach unity in the thermodynamic limit even though our approximation omits more than half of the Hilbert space. We show that the product rule is valid for any FQH state which can be written as an expectation value of parafermionic operators.

cond-mat.str-el↗