Article
Physics, Multidisciplinary
Yichen Huang
Summary: We study the fluctuations of eigenstate expectation values in a microcanonical ensemble and derive an analytical formula for the finite-size scaling of the fluctuations, assuming the eigenstate thermalization hypothesis. Our results are compared with those of Beugeling et al. (2014).
Article
Optics
Thomas Barthel, Qiang Miao
Summary: The research focuses on the behavior of entanglement entropies of eigenstates in quantum matter at different energies and subsystem sizes, as well as the universal scaling form in quantum critical regimes. By studying the harmonic lattice model, it is demonstrated how entanglement entropy follows different laws in various dimensions and how excited-state entanglement entropies are distributed around subsystem entropies of corresponding thermodynamic ensembles.
Article
Physics, Multidisciplinary
Qiang Miao, Thomas Barthel
Summary: For typical quantum many-body systems following the eigenstate thermalization hypothesis (ETH), the entanglement entropy of (almost) all energy eigenstates can be described by a single crossover function. These functions, deduced from subsystem entropies of thermal ensembles, capture the transition from ground-state entanglement regime to extensive volume-law regime and exhibit universal properties. The analytical results have been supported by numerics for noninteracting fermions in dimensions d <= 3, and confirmed for bosonic systems and nonintegrable spin chains.
PHYSICAL REVIEW LETTERS
(2021)
Article
Optics
M. R. Lambert, Shan-Wen Tsai, Shane P. Kelly
Summary: We study the resonant coupling of a fully connected quantum spin model with a small environment of noninteracting spins and investigate the memory of initial state properties at long times. We find that certain properties of the initial state, in addition to total energy, can be remembered during the dynamics, even if they are not conserved. This memory effect occurs in a specific energy range, where an eigenstate quantum phase transition (ESQPT) takes place. The memory effect at that energy is robust to system-environment coupling until the coupling changes the energy of the ESQPT. This work reveals the independence of ESQPT memory on integrability and suggests that this mechanism may have a wider generality in preventing thermalization at ESQPTs.
Article
Quantum Science & Technology
Meenu Kumari, Alvaro M. Alhambra
Summary: The study investigates the diagnostic of integrability in quantum systems through the average entanglement entropy of energy eigenstates. Analytical calculations and numerical simulations in collective spin models show that the value of average entanglement entropy could serve as a signature of integrability in the thermodynamic limit.
Article
Physics, Multidisciplinary
Miroslav Hopjan, Lev Vidmar
Summary: Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently incomplete, and it is important to establish tools for their characterization in the time domain. This study shows that a scaled survival probability, measured in units of a typical Heisenberg time, exhibits a scale-invariant behavior at eigenstate transitions in various quadratic and interacting models, which suggests intriguing similarities between localization transitions in quadratic systems and ergodicity breaking phase transitions in interacting systems.
PHYSICAL REVIEW LETTERS
(2023)
Article
Optics
Ranjan Modak, Bhabani Prasad Mandal
Summary: This study examines the properties of a non-Hermitian, non-interacting fermion model under combined PT transformation, revealing a phase transition from PT unbroken phase to broken phase. The entanglement entropy of such systems can be defined in two different ways, showcasing unique features in both phases of the system. Most notably, the entanglement entropy obtained using a combination of both left and right eigenstates exhibits exponential divergence with system size at the transition point. Meanwhile, in the PT-unbroken phase, the entanglement entropy obtained from only right (or equivalently, left) eigenstates shows behavior identical to an equivalent Hermitian system connected to the non-Hermitian system by a similarity transformation.
Article
Physics, Multidisciplinary
Qing Li, Jin-Lou Ma, Lei Tan
Summary: Research shows that the JCH system exhibits properties of a quantum chaotic system, with the emergence of quantum chaos being attributed to the competition between the hopping strength of photons and the photon-atom coupling strength. Exact diagonalization was used to verify the validity of the ETH ansatz for both diagonal and off-diagonal matrix elements of photon observables under reasonable experimental parameters.
Article
Physics, Fluids & Plasmas
Eiki Iyoda, Kazuya Kaneko, Takahiro Sagawa
Summary: In this paper, we theoretically and numerically show that the fluctuation theorem holds in both the long- and short-time regimes, even when the initial state of the bath is a single energy eigenstate of a many-body system.
Article
Physics, Fluids & Plasmas
Goran Nakerst, Masudul Haque
Summary: The study explores the effect of increasing the particle number in fixed lattice topologies in the classical or semiclassical limit, focusing on the behavior of the Bose-Hubbard system. It is found that for larger lattices, the ETH scaling of physical midspectrum eigenstates follows the ideal (Gaussian) expectation, while for smaller lattices, anomalous scaling occurs with a different exponent. Various plausible mechanisms for this anomaly are examined.
Article
Astronomy & Astrophysics
Daniel Louis Jafferis, David K. Kolchmeyer, Baur Mukhametzhanov, Julian Sonner
Summary: This paper presents evidence for a duality between Jackiw-Teitelboim gravity and a two-matrix model, and analyzes their correlations. The study shows that in certain cases, gravitational correlators can be reproduced using matrix models. However, the presence of UV divergence suggests that the matrix models are perturbatively unstable in some cases.
Article
Physics, Multidisciplinary
Charlie Nation, Diego Porras
Summary: This study explores how quantum dynamics in a single excitation subspace deviates from predictions of the eigenstate thermalization hypothesis (ETH). By analyzing long-time fluctuations, two-point correlation functions, and out-of-time-ordered correlators, a new relation similar to ETH is derived. Additionally, the time-dependence of equilibrium decay is computed.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Quantum Science & Technology
Qiang Miao, Thomas Barthel
Summary: With increasing subsystem size and energy, bipartite entanglement entropies of energy eigenstates cross over from the groundstate scaling to a volume law. It was previously pointed out that the entanglement entropies of almost all eigenstates follow a single crossover function when strong or weak eigenstate thermalization applies. Here, the scaling properties for integrable and non-integrable interacting spin 1/2 chains at criticality are substantiated using exact diagonalization.
Article
Physics, Particles & Fields
Yichen Huang
Summary: In this paper, the researchers investigated the relationship between the eigenstate expectation values of a local operator and the smooth function of energy density in a system as the system size diverges. They proved that for most local operators in translation-invariant quantum lattice systems, the deviations of finite-size eigenstate expectation values from the smooth function are lower bounded by 1/O(N), regardless of the integrability or chaoticity of the model. This lower bound is saturated in systems satisfying the eigenstate thermalization hypothesis.
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS
(2022)
Article
Astronomy & Astrophysics
Ning Bao, Jason Pollack, David Wakeham, Elizabeth Wildenhain
Summary: In this study, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the eigenstate thermalization hypothesis (ETH). By identifying simple operators with an algebra of low-energy observables and tracing out the high-energy Hilbert space, we demonstrate an exponential suppression of trace distance between coarse-grained eigenstates as outlined by ETH. Additionally, we show a direct translation of the BBBV lower bound on the query complexity of Grover search into a complexity-theoretic statement lower bounding the difficulty of distinguishing these reduced states.
CLASSICAL AND QUANTUM GRAVITY
(2021)
Article
Physics, Multidisciplinary
Pedro Ribeiro, Achilleas Lazarides, Masudul Haque
PHYSICAL REVIEW LETTERS
(2020)
Article
Chemistry, Multidisciplinary
Valentin L. Mueller, Yuan Yan, Oleksiy Kashuba, Bjoern Trauzettel, Mohamed Abdelghany, Johannes Kleinlein, Wouter Beugeling, Hartmut Buhmann, Laurens W. Molenkamp
Summary: Experimental investigation on the two-dimensional Dirac surface states in the three-dimensional topological insulator HgTe revealed the significant effect of electron temperature on transport properties, particularly around the minimal conductivity point. The observed nonmonotonic differential resistance in narrow channels when carriers are heated with a DC current is attributed to electron-hole scattering and Fermi energy change, dominantly influenced by a van Hove singularity in the bulk valence band. These results emphasize the importance of interband electron-hole scattering in the transport behavior of topological insulators.
Article
Multidisciplinary Sciences
Saquib Shamim, Wouter Beugeling, Pragya Shekhar, Kalle Bendias, Lukas Lunczer, Johannes Kleinlein, Hartmut Buhmann, Laurens W. Molenkamp
Summary: Researchers have successfully demonstrated the quantized spin Hall resistance in HgTe quantum wells alloyed with magnetic Mn atoms at very low temperatures, due to the Kondo screening effect. This work lays the foundation for future investigations into magnetically doped quantum spin Hall materials and the realization of chiral Majorana fermions.
NATURE COMMUNICATIONS
(2021)
Article
Chemistry, Multidisciplinary
David M. Mahler, Valentin L. Mueller, Cornelius Thienel, Jonas Wiedenmann, Wouter Beugeling, Hartmut Buhmann, Laurens W. Molenkamp
Summary: Magneto-transport measurements on gated high-mobility heterostructures containing a 60 nm layer of tensile-strained HgTe reveal the presence of well-developed Hall quantization from surface states in both n- and p-type regimes. While the n-type behavior is attributed to transport in the topological surface state, the p-type transport is shown to result from massive Volkov-Pankratov states, preventing the observation of the p-conducting topological surface state in transport experiments.
Article
Multidisciplinary Sciences
Saquib Shamim, Pragya Shekhar, Wouter Beugeling, Jan Bottcher, Andreas Budewitz, Julian-Benedikt Mayer, Lukas Lunczer, Ewelina M. Hankiewicz, Hartmut Buhmann, Laurens W. Molenkamp
Summary: This study reports the absence of transport gap in disordered two dimensional topological insulators at high magnetic fields. It is observed that at larger fields, only the quantum Hall edge channel with transverse resistance close to h/e(2) exists.
NATURE COMMUNICATIONS
(2022)
Article
Chemistry, Multidisciplinary
Arya Thenapparambil, Graciely Elias dos Santos, Chang-An Li, Mohamed Abdelghany, Wouter Beugeling, Hartmut Buhmann, Charles Gould, Song-Bo Zhang, Bjorn Trauzettel, Laurens W. Molenkamp
Summary: Fluctuations in planar magnetotransport in topological HgTe structures are caused by tilted Dirac cones and the formation of charge puddles. The tilted Dirac cones are due to the mix of the Zeeman term and quadratic contributions to the dispersion relation. A network model is developed to mimic the transport of tilted Dirac fermions in the landscape of charge puddles, and it captures the essential features of the experimental data. This model is relevant for interpreting planar magnetotransport in various topological and small bandgap materials.
Article
Physics, Fluids & Plasmas
Phillip C. Burke, Goran Nakerst, Masudul Haque
Summary: The study examines different methods of assigning temperature to energies or eigenstates in finite isolated quantum systems. It is found that the commonly used assignment based on the canonical energy-temperature relationship only depends on energy eigenvalues and not on the structure of eigenstates. The definition of temperature for eigenstates is considered by minimizing the distance between (full or reduced) eigenstate density matrices and canonical density matrices. The results show that the minimizing temperature depends on the distance measure chosen and matches the canonical temperature for the trace distance.
Article
Physics, Fluids & Plasmas
Phillip C. Burke, Masudul Haque
Summary: We investigate the comparison between the temperature calculated from the microcanonical entropy and the canonical temperature for finite isolated quantum systems. Our focus is on systems that can be numerically diagonalized exactly due to their size. We thus characterize the deviations from ensemble equivalence at finite sizes and present multiple methods to compute the microcanonical entropy, providing numerical results for the entropy and temperature obtained using these methods. We show that using an energy window with a particular energy dependence minimizes the deviations from the canonical temperature.
Article
Materials Science, Multidisciplinary
Raphael C. Vidal, Giovanni Marini, Lukas Lunczer, Simon Moser, Lena Fuerst, Julia Issing, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Charles Gould, Hartmut Buhmann, Wouter Beugeling, Giorgio Sangiovanni, Domenico Di Sante, Gianni Profeta, Laurens W. Molenkamp, Hendrik Bentmann, Friedrich Reinert
Summary: This study presents a joint experimental and theoretical investigation of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, using angle-resolved photoelectron spectroscopy and density functional theory. The results demonstrate detailed agreement with theoretical predictions, including electronic band dispersions and orbital symmetries, surface and bulk contributions, and the importance of Hg 5d states in valence-band formation. The experiments directly image the paradigmatic band inversion in HgTe, revealing its nontrivial band topology.
Article
Physics, Fluids & Plasmas
Goran Nakerst, Masudul Haque
Summary: We investigate the relationship between chaos in a Bose-Hubbard system and its classical limit. By comparing quantum measures of chaos with classical measures, we find a strong correspondence between the two cases in terms of energy and interaction strength. Unlike strongly chaotic and integrable systems, the largest Lyapunov exponent is shown to be a multivalued function of energy.
Article
Physics, Fluids & Plasmas
Masudul Haque, Paul A. McClarty, Ivan M. Khaymovich
Summary: Eigenstates of local many-body interacting systems far from spectral edges are believed to be ergodic and close to randomness, aligning with the eigenstate thermalization hypothesis and entanglement volume-law scaling. However, systematic departures from complete randomness are typically present in mid-spectrum eigenstates, partly due to spatial correlations and orthogonality to eigenstates at the spectral edge, which introduce structure to these mid-spectrum states.
Article
Materials Science, Multidisciplinary
Wouter Beugeling
Summary: The quantum spin Hall effect is a result of band inversion in topological insulators, leading to helical edge channels with finite spin Hall conductivity. A generalized notion of spin Hall conductivity is discussed in this work, where a block structure is defined in the more general k . p model using the concept of isoparity, which remains a conserved quantity under various conditions, especially in the presence of a perpendicular external magnetic field. Isoparity, fundamentally defined as the action of z -> -z on spatial and spinorial degrees of freedom, allows for the identification of two uncoupled blocks in the Hamiltonian matrix, acting as Kramers partners due to time reversal anticommutation. This approach uncovers the true meaning of 'spin' as a crystal symmetry realized by a spinorial representation.
Article
Physics, Fluids & Plasmas
Goran Nakerst, Masudul Haque
Summary: The study explores the effect of increasing the particle number in fixed lattice topologies in the classical or semiclassical limit, focusing on the behavior of the Bose-Hubbard system. It is found that for larger lattices, the ETH scaling of physical midspectrum eigenstates follows the ideal (Gaussian) expectation, while for smaller lattices, anomalous scaling occurs with a different exponent. Various plausible mechanisms for this anomaly are examined.
Article
Materials Science, Multidisciplinary
Paul A. McClarty, Masudul Haque, Arnab Sen, Johannes Richter
Article
Optics
Phillip C. Burke, Jan Wiersig, Masudul Haque
