arXiv subjects

Nicolas Regnault

Publications and source records attributed to Nicolas Regnault.

At least 91 records · Page 5Linked to original sources

arXiv2021

Universal signatures of Dirac fermions in entanglement and charge fluctuations

We investigate the entanglement entropy (EE) and charge fluctuations in models where the low energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, \emph{i.e.}, independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up to a constant prefactor. To check the validity of universality arguments, we numerically consider several models, with different geometries and number of Dirac cones, and either for strictly two-dimensional models or for gapless surface mode of three-dimensional topological insulators. We also show that the flux response does not depend on the entangling surface geometry as long as it encloses the flux. Finally we consider the universal corner contributions to the EE. We show that in the presence of corners, the Kitaev-Preskill subtraction scheme provides non-universal, geometry dependent results.

cond-mat.mes-hall↗

arXiv2021

The Impact of Observing Strategy on Cosmological Constraints with LSST

The generation-defining Vera C. Rubin Observatory will make state-of-the-art measurements of both the static and transient universe through its Legacy Survey for Space and Time (LSST). With such capabilities, it is immensely challenging to optimize the LSST observing strategy across the survey's wide range of science drivers. Many aspects of the LSST observing strategy relevant to the LSST Dark Energy Science Collaboration, such as survey footprint definition, single visit exposure time and the cadence of repeat visits in different filters, are yet to be finalized. Here, we present metrics used to assess the impact of observing strategy on the cosmological probes considered most sensitive to survey design; these are large-scale structure, weak lensing, type Ia supernovae, kilonovae and strong lens systems (as well as photometric redshifts, which enable many of these probes). We evaluate these metrics for over 100 different simulated potential survey designs. Our results show that multiple observing strategy decisions can profoundly impact cosmological constraints with LSST; these include adjusting the survey footprint, ensuring repeat nightly visits are taken in different filters and enforcing regular cadence. We provide public code for our metrics, which makes them readily available for evaluating further modifications to the survey design. We conclude with a set of recommendations and highlight observing strategy factors that require further research.

astro-ph.CO↗

arXiv2021

TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moiré Systems with and without Displacement Field

We derive the Hamiltonian for trilayer moiré systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror-symmetry with respect to the middle layer. We provide a full symmetry analysis of the non-interacting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high velocity Dirac fermions, and we identify a hidden non-local symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of non-interacting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wavefunctions and derive the full many-body Hamiltonian of the system. We also provide an efficient parameterization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the $\mathrm{U} \left( 2 \right) \times \mathrm{U} \left( 2 \right)$ spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large $\mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right) \times \mathrm{U} \left( 4 \right)$ symmetry in the chiral limit. Moreover, by identifying a new symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

cond-mat.str-el↗

arXiv2021

An $O(N)$ $Ab~initio$ Calculation Scheme for Large-Scale Moiré Structures

We present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for ground state is performed with $O(N)$ Krylov subspace method implemented in OpenMX. Secondly, the crystal momentum dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures at the first magic angle ($θ=1.08^\circ$) and other three larger ones with satisfied accuracy on affordable costs. The band structures are in good agreement with those from tight binding models, continuum models, plane-wave pseudo-potential based $ab~initio$ calculations, and the experimental observations. This efficient two-step method is to play a crucial role in other twisted two-dimensional materials, where the band structures are much more complex than graphene and the effective model is hard to be constructed.

cond-mat.mes-hall↗

arXiv2020

Hofstadter Topology: Non-crystalline Topological Materials at High Flux

The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding $\sim 10^4$ T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of remarkable possible phases emerges. Remarkably, we find topological phases which cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with nonzero Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with nontrivial Kane-Mele invariant produces a 3D TI or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of two-fold rotation and time-reversal and show that there exists a 3D higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group which exists at rational values of the flux. The advent of Moiré lattices also renders our work relevant experimentally. In Moiré lattices, it is possible for fields of order $1-30$ T to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

cond-mat.mes-hall↗

arXiv2020

Quantum Many-body Scars in a Landau Level on a Thin Torus

We study a kinetically constrained pair hopping model that arises within a Landau level in the quantum Hall effect. At filling $ν= 1/3$, the model exactly maps onto the so-called "PXP model", a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors $ν= p/(2p+1)$, and show that the model is equivalent to non-integrable spin-chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.

cond-mat.str-el↗

arXiv2020

High-throughput calculations of magnetic topological materials

The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators, have directed fundamental research in solid-state materials. Topological quantum chemistry has enabled the understanding of and the search for paramagnetic topological materials. Using magnetic topological indices obtained from magnetic topological quantum chemistry (MTQC), here we perform a high-throughput search for magnetic topological materials based on first-principles calculations. We use as our starting point the Magnetic Materials Database on the Bilbao Crystallographic Server, which contains more than 549 magnetic compounds with magnetic structures deduced from neutron-scattering experiments, and identify 130 enforced semimetals (for which the band crossings are implied by symmetry eigenvalues), and topological insulators. For each compound, we perform complete electronic structure calculations, which include complete topological phase diagrams using different values of the Hubbard potential. Using a custom code to find the magnetic co-representations of all bands in all magnetic space groups, we generate data to be fed into the algorithm of MTQC to determine the topology of each magnetic material. Several of these materials display previously unknown topological phases, including symmetry-indicated magnetic semimetals, three-dimensional anomalous Hall insulators and higher-order magnetic semimetals. We analyse topological trends in the materials under varying interactions: 60 per cent of the 130 topological materials have topologies sensitive to interactions, and the others have stable topologies under varying interactions. We provide a materials database for future experimental studies and open-source code for diagnosing topologies of magnetic materials.

cond-mat.mtrl-sci↗

arXiv2020

Fractional Chiral Hinge Insulator

We propose and study a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two non-interacting second order topological insulators with chiral hinge modes at half filling. We use large-scale variational Monte Carlo computations to characterize the model states via the entanglement entropy and charge-spin-fluctuations. We show that the FCHI possesses fractional chiral hinge modes characterized by a central charge $c=1$ and Luttinger parameter $K=1/2$, like the edge modes of a Laughlin $1/2$ state. By changing the boundary conditions for the underlying fermions, we investigate the topological degeneracy of the FCHI. Within the range of the numerically accessible system sizes, we observe a non-trivial topological degeneracy. A more numerically pristine characterization of the bulk topology is provided by the topological entanglement entropy (TEE) correction to the area law. While our computations indicate a vanishing bulk TEE, we show that the gapped surfaces host a two-dimensional topological order with a TEE per surface compatible with half that of a Laughlin $1/2$ state, a value that cannot be obtained from topological quantum field theory.

cond-mat.str-el↗

arXiv2020

Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to construct two-dimensional (2D) topological quasi-flat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands. The flat band connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasi-flat and gapped from the dispersive bands. By studying a series of specific line graphs and split graphs of bipartite lattices, we find that (i) if the flat band (without SOC) has inversion or $C_2$ symmetry and is non-degenerate, then the resulting quasi-flat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists an SOC potential such that the resulting quasi-flat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasi-flat bands in 2D crystalline materials and meta-materials.

cond-mat.mes-hall↗

arXiv2020

Large Classes of Quantum Scarred Hamiltonians from Matrix Product States

Motivated by the existence of exact many-body quantum scars in the AKLT chain, we explore the connection between Matrix Product State (MPS) wavefunctions and many-body quantum scarred Hamiltonians. We provide a method to systematically search for and construct parent Hamiltonians with towers of exact eigenstates composed of quasiparticles on top of an MPS wavefunction. These exact eigenstates have low entanglement in spite of being in the middle of the spectrum, thus violating the strong Eigenstate Thermalization Hypothesis (ETH). Using our approach, we recover the AKLT chain starting from the MPS of its ground state, and we derive the most general nearest-neighbor Hamiltonian that shares the AKLT quasiparticle tower of exact eigenstates. We further apply this formalism to other simple MPS wavefunctions, and derive new families of Hamiltonians that exhibit AKLT-like quantum scars. As a consequence, we also construct a scar-preserving deformation that connects the AKLT chain to the integrable spin-1 pure biquadratic model. Finally, we also derive other families of Hamiltonians that exhibit new types of exact quantum scars, including a $U(1)$-invariant perturbed Potts model.

cond-mat.str-el↗

arXiv2020

Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices

Coupled-wire constructions offer particularly simple and powerful models to capture the essence of strongly correlated topological phases of matter. They often rely on effective theories valid in the low-energy and strong coupling limits, which impose severe constraints on the physical systems where they could be realized. We investigate the microscopic relevance of a class of coupled-wire models and their possible experimental realization in cold-atom experiments. We connect with earlier results and prove the emergence of fractional quantum Hall states in the limit of strong inter-wire tunneling. Contrary to previous studies relying on renormalization group arguments, our microscopic approach exposes the connection between coupled-wire constructions and model wavefunctions in continuum Landau levels. Then, we use exact diagonalization methods to investigate the appearance of these fractional quantum Hall states in more realistic settings. We examine the parameter regimes where these strongly correlated phases arise, and provide a way to detect their appearance in cold-atom experiments through standard time-of-flight measurements. Motivated by this experimental probe, we finally propose a realization of our model with cold-atom in spin-dependent optical lattices. Our estimates show that the previous fractional quantum Hall phases lie within experimentally accessible parameter regimes, giving a viable route towards their experimental study.

cond-mat.str-el↗

arXiv2020

Quantum scars of bosons with correlated hopping

Recent experiments on Rydberg atom arrays have found evidence of anomalously slow thermalization and persistent density oscillations, which have been interpreted as a many-body analog of the phenomenon of quantum scars. Periodic dynamics and atypical scarred eigenstates originate from a "hard" kinetic constraint: the neighboring Rydberg atoms cannot be simultaneously excited. Here we propose a realization of quantum many-body scars in a 1D bosonic lattice model with a "soft" constraint in the form of density-assisted hopping. We discuss the relation of this model to the standard Bose-Hubbard model and possible experimental realizations using ultracold atoms. We find that this model exhibits similar phenomenology to the Rydberg atom chain, including weakly entangled eigenstates at high energy densities and the presence of a large number of exact zero energy states, with distinct algebraic structure.

quant-ph↗

arXiv2020

Detection of Topological Materials with Machine Learning

Databases compiled using ab-initio and symmetry-based calculations now contain tens of thousands of topological insulators and topological semimetals. This makes the application of modern machine learning methods to topological materials possible. Using gradient boosted trees, we show how to construct a machine learning model which can predict the topology of a given existent material with an accuracy of 90%. Such predictions are orders of magnitude faster than actual ab-initio calculations. Through extensive testing of different models we determine which properties help detect topological materials. We identify the sources of our model's errors and we discuss approaches to overcome them.

cond-mat.mtrl-sci↗

arXiv2020

Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars

We revisit the $η$-pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. $η$-pairing occurs due to an algebraic structure known as a Spectrum Generating Algebra (SGA), giving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original $η$-pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a Restricted Spectrum Generating Algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of the original model as eigenstates. The states of the surviving tower exhibit a sub-thermal entanglement entropy, and we analytically obtain parameter regimes for which they lie in the bulk of the spectrum, showing that they are exact quantum many-body scars. The RSGA framework also explains the equally spaced towers of eigenstates in several well-known models of quantum scars, including the AKLT model.

cond-mat.str-el↗

arXiv2020

Fragile Phases As Affine Monoids: Classification and Material Examples

Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an Elementary Band Representation (Atomic Limit Band) splits into a particular set of bands. We obtain, for the first time, a complete classification of the fragile topological phases which can be diagnosed by symmetry eigenvalues, to find an incredibly rich structure which far surpasses that of stable/strong topological states. We find and enumerate all hundreds of thousands of different fragile topological phases diagnosed by symmetry eigenvalues (available at http://www.cryst.ehu.es/html/doc/FragileRoots.pdf), and link the mathematical structure of these phases to that of Affine Monoids in mathematics. Furthermore, we predict and calculate, for the first time, (hundred of realistic) materials where fragile topological bands appear, and show-case the very best ones.

cond-mat.mes-hall↗

arXiv2019

Fermionic tensor networks for higher order topological insulators from charge pumping

We apply the charge pumping argument to fermionic tensor network representations of d-dimensional topological insulators (TIs) to obtain tensor network states for (d+1)-dimensional TIs. We exemplify the method by constructing a two-dimensional projected entangled pair states (PEPS)for a Chern insulator starting from a matrix product state (MPS) in d=1 describing pumping in the Su-Schrieffer-Heeger (SSH) model. In extending the argument to second-order TIs, we build a three-dimensional TNS for a chiral hinge TI from a PEPS in d=2 for the obstructed atomic insulator (OAI) of the quadrupole model. The (d+1)-dimensional TNSs obtained in this way have a constant bond dimension inherited from the d-dimensional TNSs in all but one spatial direction, making them candidates for numerical applications. From the d-dimensional models, we identify gapped next-nearest neighbour Hamiltonians interpolating between the trivial and OAI phases of the fully dimerized SSH and quadrupole models, whose ground states are given by an MPS and a PEPS with a constant bond dimension equal to 2, respectively.

cond-mat.str-el↗

arXiv2019

Thermalization and its absence within Krylov subspaces of a constrained Hamiltonian

We study the quantum dynamics of a simple translation invariant, center-of-mass (CoM) preserving model of interacting fermions in one dimension (1D), which arises in multiple experimentally realizable contexts. We show that this model naturally displays the phenomenology associated with fractonic systems, wherein single charges can only move by emitting dipoles. This allows us to demonstrate the rich Krylov fractured structure of this model, whose Hilbert space shatters into exponentially many dynamically disconnected subspaces. Focusing on exponentially large Krylov subspaces, we show that these can be either be integrable or non-integrable, thereby establishing the notion of Krylov-restricted thermalization. We analytically find a tower of integrable Krylov subspaces of this Hamiltonian, all of which map onto spin-1/2 XX models of various system sizes. We also discuss the physics of the non-integrable subspaces, where we show evidence for weak Eigenstate Thermalization Hypothesis (ETH) restricted to each non-integrable Krylov subspace. Further, we show that constraints in some of the thermal Krylov subspaces cause the long-time expectation values of local operators to deviate from behavior typically expected from translation-invariant systems. Finally, we show using a Schrieffer-Wolff transformation that such models naturally appear as effective Hamiltonians in the large electric field limit of the interacting Wannier-Stark problem, and comment on connections of our work with the phenomenon of Bloch many-body localization.

cond-mat.str-el↗

arXiv2019

Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models

We study the properties of the entanglement spectrum in gapped non-interacting non-Hermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in non-Hermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the many-body state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the many-body right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.

cond-mat.mes-hall↗