A5049927722- Quantum many-body systems
- Physics of Superconductivity and Magnetism
- Quantum and electron transport phenomena
- Cold Atom Physics and Bose-Einstein Condensates
- Advanced Condensed Matter Physics
- Topological Materials and Phenomena
- Quantum Computing Algorithms and Architecture
- Theoretical and Computational Physics
- Quantum, superfluid, helium dynamics
- Quantum Information and Cryptography
- Opinion Dynamics and Social Influence
- Advanced Thermodynamics and Statistical Mechanics
- Quantum chaos and dynamical systems
- Model Reduction and Neural Networks
- Computational Physics and Python Applications
- Quantum optics and atomic interactions
- Spectroscopy and Quantum Chemical Studies
- Quantum Mechanics and Applications
- Spectral Theory in Mathematical Physics
- Algebraic structures and combinatorial models
- Tensor decomposition and applications
- Gas Dynamics and Kinetic Theory
- Game Theory and Applications
- Atomic and Subatomic Physics Research
- Quantum Chromodynamics and Particle Interactions
Technical University of Munich
2017-2025
Munich Center for Quantum Science and Technology
2019-2025
Institute for Advanced Study
2019-2024
Flatiron Health (United States)
2022
Flatiron Institute
2022
University of Birmingham
2022
Ludwig-Maximilians-Universität München
2013-2021
Max Planck Institute for the Physics of Complex Systems
2008-2019
Max Planck Society
2006-2018
California Institute of Technology
2018
We show that the Haldane phase of S=1 chains is characterized by a double degeneracy entanglement spectrum. The protected set symmetries (either dihedral group $\pi$-rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either boundary to another, "topologically trivial", crossed, symmetry broken. More generally, these results offer scheme classify gapped phases one dimensional systems. Physically, spectrum can observed...
An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution simple (unentangled) initial states studied numerically for spinless fermions in one dimension described the random-field XXZ Hamiltonian. Interactions induce dramatic change propagation entanglement smaller particles. For even weak interactions, when thought to many-body phase, shows neither nor diffusive behavior but grows without...
We discuss the characterization and stability of Haldane phase in integer spin chains on basis simple, physical arguments. find that an odd-$S$ is a topologically nontrivial which protected by any one following three global symmetries: (i) dihedral group $\ensuremath{\pi}$ rotations about $x$, $y$, $z$ axes, (ii) time-reversal symmetry ${S}^{x,y,z}\ensuremath{\rightarrow}\ensuremath{-}{S}^{x,y,z}$, (iii) link inversion (reflection bond center), consistent with previous results [Phys. Rev. B...
Thermalization and scrambling are the subject of much recent study from perspective many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), field theory holography. We tackle this problem in 1D spin-chains evolving under random local unitary circuits prove a number exact results on behavior out-of-time-ordered commutators (OTOCs), entanglement growth setting. These follow observation that spreading operators is described by `hydrodynamical' equation motion, despite...
Many-body localization occurs in isolated quantum systems when Anderson persists the presence of finite interactions. Despite strong evidence for existence a many-body transition, reliable extraction critical disorder strength is difficult due to large drift with system size studied quantities. In this Letter, we explore two entanglement properties that are promising study transition: variance half-chain entropy exact eigenstates and long time change after local quench from an eigenstate. We...
The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe framework for classifying phases one-dimensional interacting fermions, focusing spinless fermions with time-reversal symmetry particle number parity conservation, using concepts entanglement. In agreement example presented by L. Fidkowski A. Kitaev [Phys. Rev. B 81, 134509 (2010)], find that in the presence there are only eight distinct which obey...
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool condensed matter theory chemistry. these lecture notes, we combine a compact review basic TPS concepts with introduction versatile tensor library for Python (TeNPy) [https://github.com/tenpy/tenpy]. As concrete examples, consider MPS time-evolving block...
We show that the combination of charge and dipole conservation---characteristic fracton systems---leads to an extensive fragmentation Hilbert space, which in turn can lead a breakdown thermalization. As concrete example, we investigate out-of-equilibrium dynamics one-dimensional spin-1 models conserve (total $S^z$) its associated moment. First, consider minimal model including only three-site terms find infinite temperature auto-correlation saturates finite value---showcasing non-thermal...
The discovery of topological order has revolutionized the understanding quantum matter in modern physics and provided theoretical foundation for many error correcting codes. Realizing topologically ordered states proven to be extremely challenging both condensed synthetic systems. Here, we prepare ground state toric code Hamiltonian using an efficient circuit on a superconducting processor. We measure entanglement entropy near expected value $\ln2$, simulate anyon interferometry extract...
The scrambling of quantum information in closed many-body systems, as measured by out-of-time-ordered correlation functions (OTOCs), has lately received considerable attention. Recently, a hydrodynamical description OTOCs emerged from considering random local circuits, aspects which are conjectured to be universal ergodic even without randomness. Here we extend this approach systems with locally conserved quantities (e.g., energy). We do unitary circuits U$(1)$ charge and argue, numerical...
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more than non-critical states. Standard algorithms for one-dimensional construct model with limited entanglement, which are a worse approximation to others. We give quantitative theory previously observed scaling behavior resulting from finite at criticality: the is only superficially similar finite-size scaling, and has different physical origin. find finite-entanglement...
A topological phase is a of matter which cannot be characterized by local order parameter. It has been shown that gapped symmetric phases in one-dimensional (1D) systems can completely using tools related to projective representations the symmetry groups. We explain two ways detect these protected 1D. First, we give numerical approach for directly extracting from matrix-product state representation. Second, derive nonlocal parameters time-reversal and inversion symmetry, discuss generalized...
We introduce a numerical algorithm to simulate the time evolution of matrix product state under long-ranged Hamiltonian. In effectively one-dimensional representation system by states, interactions are necessary not just many physical but also higher-dimensional problems with short-ranged interactions. Since our method overcomes restriction Hamiltonians most existing methods, it proves particularly useful for studying dynamics both power-law interacting systems, such as Coulombic and dipolar...
Abstract Universal quantum computers are potentially an ideal setting for simulating many-body dynamics that is out of reach classical digital computers. We use state-of-the-art IBM to study paradigmatic examples condensed matter physics—we simulate the effects disorder and interactions on particle transport, as well correlation entanglement spreading. Our benchmark results show quality current machines below what necessary quantitatively accurate continuous-time observables reachable system...
The antiferromagnetic spin-$1/2$ Heisenberg model on a kagome lattice is one of the most paradigmatic models in context spin liquids, yet precise nature its ground state not understood. We use large scale density matrix normalization group simulations (DMRG) infinitely long cylinders and find indications for formation gapless Dirac liquid. First, we adiabatic flux insertion to demonstrate that gap much smaller than estimated from previous DMRG simulation. Second, momentum dependent...
We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to strong electric field. In the non-interacting case, due Wannier-Stark localization, single-particle wave functions are exponentially localized even though model has no quenched disorder. show that this system remains in presence of interactions exhibits physics analogous models conventional many-body localization (MBL). particular, entanglement entropy grows...
We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall Hamiltonian. To find the set of degenerate ground states, we employ infinite density matrix renormalization group method based on matrix-product state representation states an cylinder. study localized quasiparticles chosen charge, use pairs as boundary conditions for group. then wave function obtained cylinder geometry can be adapted torus arbitrary...
The current generation of noisy intermediate scale quantum computers introduces new opportunities to study many-body systems. In this paper, we show that circuits can provide a dramatically more efficient representation than classical numerics the states generated under non-equilibrium dynamics. For circuits, perform both real- and imaginary-time evolution using an optimization algorithm is feasible on near-term computers. We benchmark algorithms by finding ground state simulating global...
The authors present a unified perspective on large class of one-dimensional symmetry-protected topological phases. Characterizing critical points between such phases leads to conjecture lower bound the central charge in terms phase-specific edge mode dimension.
Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing notion `statistically localized integrals motion' (SLIOM), whose eigenvalues label connected components space. SLIOMs are not spatially in operator sense, but appear sub-extensive regions when their expectation value is taken typical states with finite density particles. We illustrate this general concept...
The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that conserving the dipole moment an associated charge, or even higher-moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modeling time evolution as cellular automata for specific cases dipole- and quadrupole conservation, numerically find distinct anomalous exponents relaxation. We explain these findings by...
We introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, symmetry properties of low-energy conformal field theory (CFT) provide discrete invariants, establishing notion symmetry-enriched quantum criticality. The charges nonlocal scaling operators, or more generally defects, are imply presence localized edge modes. primarily focus on $1+1d$ case where has a degeneracy, whose finite-size splitting can be exponential algebraic in...
Quantum computers promise to perform computations beyond the reach of modern with profound implications for scientific research. Due remarkable technological advances, small scale devices are now becoming available use. One most apparent applications such a device is study complex many-body quantum systems, where classical unable deal generic exponential complexity states. Even zero-temperature equilibrium phases matter and transitions between them have yet be fully classified, topologically...
Topology in quantum many-body systems has profoundly changed our understanding of phases matter. The model that played an instrumental role elucidating these effects is the antiferromagnetic spin-1 Haldane chain1,2. Its ground state a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In bulk, it characterized by vanishing two-point correlations, gapped excitations and characteristic non-local order parameter3,4. More recently been...