We propose a procedure that characterizes free-fermion or interacting multipolar higher-order topological phases via their bulk entanglement structure. To this end, we construct nested entanglement Hamiltonians by first applying an entanglement cut to the ordinary many-body ground state, and then iterating the procedure by applying further entanglement cuts to the (assumed unique) ground state of the entanglement Hamiltonian. We argue that an $n$-th order multipolar topological phase can be characterized by the features of its $n$-th order nested entanglement Hamiltonian e.g., degeneracy in the entanglement spectrum. We explicitly compute nested entanglement spectra for a set of higher-order fermionic and bosonic multipole phases and show that our method successfully identifies such phases.
Motivated by the recent development in strong spin-orbit-coupled materials, we consider the dipole-octupole doublets on the triangular lattice. We propose the most general interaction between these unusual local moments. Due to the spin-orbit entanglement and the special form of its wavefunction, the dipole-octupole doublet has a rather peculiar property under the lattice symmetry operation. As a result, the interaction is highly anisotropic in the pseudospin space, but remarkably, is uniform spatially. We analyze the ground state properties of this generic model and emphasize the hidden multi…
Basal-plane anisotropy of field-induced multipolar order in tetragonal CeRh$_2$As$_2$
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Université Grenoble Alpes, CEA, Grenoble-INP, IRIG, Pheliqs（格勒诺布尔阿尔卑斯大学）；Institute for Solid State and Materials Physics, Dresden University of Technology（德累斯顿工业大学固态与材料物理研究所）；Laboratoire National des Champs Magnétiques Intenses (LNCMI-EMFL), CNRS, Université Grenoble Alpes（法国国家强磁场实验室）；Université Grenoble Alpes, CNRS, Institut Néel（格勒诺布尔阿尔卑斯大学尼埃尔研究所）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）
Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as "hidden orders" due to the formidable task of detecting them with conventional probes. Examples of such hidden orders include spin-nematic order in quantum magnets, and quadrupolar or higher multipolar orders in various correlated quantum materials. In this work, we theoretically propose that the study of magnetostriction provides a powerful and novel tool to directly detect higher-order multipolar symmetry breaking $-$ such as the elusive octupolar order $-$ by examining its scalin…
The main question we address is how to probe the fractionalized excitations of a quantum spin liquid (QSL), for example, in the Kitaev honeycomb model. By analyzing the energy spectrum and entanglement entropy, for antiferromagnetic couplings and a field along either [111] or [001], we find a gapless QSL phase sandwiched between the non-Abelian Kitaev QSL and polarized phases. Increasing the field strength towards the polarized limit destroys this intermediate QSL phase, resulting in a considerable reduction in the number of frequency modes and the emergence of a beating pattern in the local d…
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 s…
We examine the time evolution of the entanglement spectrum of a small subsystem of a non-integrable spin chain following a quench from a product state. We identify signatures in this entanglement spectrum of the distinct dynamical velocities (related to entanglement and operator spreading) that control thermalization. We show that the onset of level repulsion in the entanglement spectrum occurs on different timescales depending on the "entanglement energy", and that this dependence reflects the shape of the operator front. Level repulsion spreads across the entire entanglement spectrum on time…
We study one-dimensional disordered fermions that either undergo metal-insulator transitions or topological phase transitions to become trivial Anderson insulators. We focus on using entanglement to elucidate how the spatial, momentum, and internal degrees of freedom of fermions are affected by the presence of disorder in such cases. We develop entanglement tools that reveal the existence of metallic states in the presence of disorder and further show clear signatures of the corresponding localization transition even in the presence of interactions. In systems where the internal degrees of fre…
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…
Hidden Magnetic Octupolar Order driven by Spin-Orbit coupling in KFeF$_3$
University of Warwick（华威大学）；Durham University（杜伦大学）；University of Edinburgh（爱丁堡大学）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；Institut Laue-Langevin（朗之万研究所）
Quantum spin liquids (QSL) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its non-locality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density-matrix renormalization group, we reveal the entangl…
We consider a spin ladder model which is known to have matrix product states as exact ground states with spin liquid characteristics. The model has two critical-point transitions at the parameter values u=0 and infinity. We study the variation of entanglement and fidelity measures in the ground states as a function of u and specially look for signatures of quantum phase transitions at u=0 and infinity. The two different entanglement measures used are S(i) (the single-site von Neumann entropy) and S(i, j) (the two-body entanglement). At the quantum critical point (QCP) u=infinity, the entanglem…
Entangled solid state systems have gained a great deal of attention due to their fruitful applications in modern quantum technologies. Herein, detection of entanglement content from experimental magnetic susceptibility and specific heat data is reported for NH4CuPO4.H2O in its solid state crystalline form. NH4CuPO4.H2O is a prototype of Heisenberg spin 1/2 dimer system. Temperature dependent magnetic susceptibility and specific data are fitted to an isolated dimer model and the exchange coupling constant is determined. Field dependent magnetization isotherms taken at different temperatures are…
The many-body localization transition is a dynamical quantum phase transition between a localized and an extended phase. We study this transition in the XXZ model with disordered magnetic field and focus on the time evolution following a global quantum quench. While the dynamics of the bipartite entanglement and spin fluctuations are already known to provide insights into the nature of the many-body localized phases, we discuss the relevance of these quantities in the context of the localization transition. In particular, we observe that near the transition the long time limits of both quantit…
Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In a previous work, we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-p…
We study the entanglement entropy and entanglement spectrum of the paradigmatic Bose-Hubbard model, describing strongly correlated bosons on a lattice. The use of a controlled approximation - the slave-boson approach - allows us to study entanglement in all regimes of the model (and, most importantly, across its superfluid/Mott-insulator transition) at a minimal cost. We find that the area-law scaling of entanglement -- verified in all the phases -- exhibits a sharp singularity at the transition. The singularity is greatly enhanced when the transition is crossed at fixed, integer filling, due …
Recent proposals of measuring bipartite Renyi entropy experimentally involve techniques that hold exactly for non-interacting quantum particles. Here we consider the difference between such measurements and the actual Renyi entropy for ground state fermion ab initio molecular systems. To calculate various entanglement measures we extended several different techniques for use with variational Monte Carlo, Hartree-Fock and quantum chemistry methods. Our results show that in systems with strong electron correlations the Renyi entropy may not be accurately determined with the proposed measurements…
We derive a general relation between the non-analyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by T. R. de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were…
It is generally difficult to experimentally distinguish magnetic multipolar orders in spin systems. Recently, it was proposed that the temperature dependence of the nuclear magnetic resonance relaxation rate 1/T_1 can involve an indirect, but clear signature of the field-induced spin nematic or multipolar Tomonaga-Luttinger (TL) liquid phase [Phys. Rev. B79, 060406(R) (2009)]. In this paper, we evaluate accurately the field and temperature dependence of 1/T_1 in spin-1/2 frustrated J1-J2 chains combining field-theoretical techniques with numerical data. Our results demonstrate that isotherms o…
Momentum-Space Entanglement Signatures and Spinon Breakdown in the $J_1$-$J_2$ Zig-Zag Heisenberg Chain
Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ctd.qmat, Universität Würzburg（维尔茨堡大学理论与天体物理研究所及维尔茨堡-德累斯顿卓越集群ctd.qmat）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）
Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigen-mode in a one-dimensional free fermion model that undergoes a delocalized-localized phase transition. In this numerical study, we show that SPEE of entanglement Hamiltonian eigen-mode has the same behavior as EPEE of Hamiltonian eigen-mode at the Fermi level: as we go from delocalized phase toward localized phase, SPEE of both modes decreases in the same manner. Furthermore, fluctuations of SPEE of entanglement Hamiltonian eigen-mode -- which can be obtained through the calculation of moments of SPEE -…
The transition from a gapless liquid to a gapped dimerized ground state that occurs in the frustrated antiferromagnetic Majumdar-Ghosh (or $J_1-J_2$ Heisenberg) model is revisited from the point of view of entanglement. We study the evolution of entanglement spectra, a "projected subspace" block entropy, and concurrence in the Schmidt vectors through the transition. The standard tool of Schmidt decomposition along with the existence of the unique MG point where the ground states are degenerate and known exactly, suggests the projection into two orthogonal subspaces that is useful even away fro…
We study operator entanglement measures of the unitary evolution operators of (1+1)-dimensional conformal field theories (CFTs), aiming to uncover their scrambling and chaotic behaviors. In particular, we compute the bi-partite and tri-partite mutual information for various configurations of input and output subsystems, and as a function of time. We contrast three different CFTs: the free fermion theory, compactified free boson theory at various radii, and CFTs with holographic dual. We find that the bi-partite mutual information exhibits distinct behaviors for these different CFTs, reflecting…
Clustered quantum materials provide a new platform for the experimental study of many-body entanglement. Here we address a simple model of a single-molecule nano-magnet featuring N interacting spins in a transverse field. The field can induce an entanglement transition (ET). We calculate the magnetisation, low-energy gap and neutron-scattering cross-section and find that the ET has distinct signatures, detectable at temperatures as high as 5% of the interaction strength. The signatures are stronger for smaller clusters.
BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains: entanglement and correlation signatures from DMRG and effective-pairing theory
Charles University（查理大学）；São Paulo State University (UNESP)（圣保罗州立大学）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）
We numerically investigate the link between the delocalization-localization transition and entanglement in a disordered long-range hopping model of spinless fermions by studying various static and dynamical quantities. This includes the inverse participation ratio, level-statistics, entanglement entropy and number fluctuations in the subsystem along with quench and wave-packet dynamics. Finite systems show delocalized, quasi-localized and localized phases. The delocalized phase shows strong area-law violation whereas the (quasi)localized phase adheres to (for large subsystems) the strict area …
We study the entanglement spectrum of topological systems hosting non-Abelian anyons. Akin to energy levels of a Hamiltonian, the entanglement spectrum is composed of symmetry multiplets. We find that the ratio between different eigenvalues within one multiplet is universal and is determined by the anyonic quantum dimensions. This result is a consequence of the conservation of the total topological charge. For systems with non-Abelian topological order, this generalizes known degeneracies of the entanglement spectrum, which are hallmarks of topological states. Experimental detection of these e…
We study the field dependence of the entanglement of formation in anisotropic S=1/2 antiferromagnetic chains and two-leg ladders displaying a T=0 field-driven quantum phase transition. The analysis is carried out via Quantum Monte Carlo simulations. At zero temperature the entanglement estimators show abrupt changes at and around criticality, vanishing below the critical field, in correspondence with an exactly factorized state, and then immediately recovering a finite value upon passing through the quantum phase transition. At the quantum critical point, a deep minimum in the pairwise-to-glob…
We study the field dependence of the entanglement of formation in anisotropic S=1/2 antiferromagnetic chains displaying a T=0 field-driven quantum phase transition. The analysis is carried out via Quantum Monte Carlo simulations. At zero temperature the entanglement estimators show abrupt changes at and around criticality, vanishing below the critical field, in correspondence with an exactly factorized state, and then immediately recovering a finite value upon passing through the quantum phase transition. At the quantum critical point, a deep minimum in the pairwise-to-global entanglement rati…
We investigate the evolution of complexity and entanglement following a quench in a one-dimensional topological system, namely the Su-Schrieffer-Heeger model. We demonstrate that complexity can detect quantum phase transitions and shows signatures of revivals; this observation provides a practical advantage in information processing. We also show that the complexity saturates much faster than the entanglement entropy in this system, and we provide a physical argument for this. Finally, we demonstrate that complexity is a less sensitive probe of topological order, compared with measures of enta…
Phase transitions at a finite (i.e. non-zero) temperature are typically dominated by classical correlations, in contrast to zero temperature transitions where quantum mechanics plays an essential role. Therefore, it is natural to ask if there are any signatures of a finite temperature phase transition in measures that are sensitive only to quantum correlations. Here we study one such measure, namely, entanglement negativity, across finite temperature phase transitions in several exactly solvable Hamiltonians and find that it is a singular function of temperature across the transition. As an as…
