Our group seminar features talks on current research topics from the field of Quantum Information and Quantum Many-Body Physics, and in particular Tensor Networks, given both by group members and by external guest speakers.

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2023 Summer Semester

During the 2023 summer semester, the seminar generally takes place in person according to the schedule and details listed below. In addition, seminar talks might occasionally be given online as announced here.

Paul Brehmer (RWTH Aachen University)

Reduced basis modeling of quantum spin systems based on DMRG
Abstract: Within the reduced basis modeling approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on density-matrix-renormalization-group (DMRG) calculations. Once the reduced basis is computed, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

Nick Jones (University of Oxford)

The MPS skeleton and exact results in topological chains
Abstract: Matrix-product states (MPS) have proven to be tremendously useful theoretical and practical tools. The MPS skeleton of a phase diagram is the family of Hamiltonians that have exact (finite-bond-dimension) MPS ground states in the thermodynamic limit. I will characterise this skeleton in a class of topological free-fermion chains, unearthing an interesting intersection between two rather different notions of exact solvability. As well as outlining the construction of the MPS ground state on the skeleton, I will explain how, on the MPS skeleton, we can find exact closed formulas for string-correlation functions in the ground state (order parameters for the different phases) and have an analytic method to compute the entanglement spectrum of a finite subsystem.
Based on arxiv:2105.12143 with Julian Bibo, Bernhard Jobst, Frank Pollmann, Adam Smith and Ruben Verresen and arxiv:2105.13359 with Ruben Verresen.

(date/time/location: 20.02.2023, 14:30, Boltzmanngasse 5, 5th floor, seminar room nr. 3510)

Zhao Zhang (SISSA Trieste)

Beyond area-law entanglement in higher dimensions and holographic tensor networks
Abstract: Height models and random tiling are well-studied objects in classical statistical mechanics and combinatorics that lead to many interesting phenomena, such as arctic curve, limit shape and Kadar-Parisi-Zhang scaling. We introduce quantum dynamics to the classical hexagonal dimer, six-, and nineteen-vertex models to construct frustration-free Hamiltonians with unique ground state being a superposition of discrete random surfaces subject to a Dirichlet boundary configuration. The local Hilbert space is further decorated by a color degree of freedom, matched in pairs between lattice sites of the same height, generating long range entanglement that makes area law violation of entanglement entropy possible. The scaling of entanglement entropy between half systems is analyzed with the gradient surface tension in the scaling limit and under a q-deformation that weighs random surfaces by the volume below, it undergoes a phase transition from area law to volume scaling. At the critical point, the scaling is L logL due to the so-called "entropic repulsion” of Gaussian free fields conditioned to stay nonnegative. An exact holographic tensor network description of the ground state is proposed with one extra dimension perpendicular to the lattice. I will also discuss an alternative realisation with vertex models, inhomogeneous deformation to obtain sub-volume intermediate scaling, and possible generalizations to higher dimension.

(date/time/location: 23.02.2023, 14:30, Erwin Schrödinger lecture room, Boltzmanngasse 5, 5th floor, room 3500)

Jared Jeyaretnam (University College London)

Symmetry-protected topological order and strong zero modes in non-ergodic systems
Abstract: At zero temperature, symmetry-protected topological (SPT) order can encode quantum information in an edge strong zero mode, robust to perturbations respecting some symmetry. On the other hand, phenomena like many-body localisation (MBL) and quantum scarring can arrest the approach to thermal equilibrium, contrary to the ergodic dynamics expected of generic quantum systems. This raises the possibility that by combining SPT order with such ergodicity breaking phenomena, one might be able to construct a quantum memory that is robust at finite temperature.
In the first part of this talk, I will look at an interacting spin-1/2 chain hosting SPT order, identifying long-lived bulk coherence in the dynamics and the quantum scars responsible, and show that these scars exhibit signatures of SPT order even at finite energy density.
In the second part of this talk, I will focus on a topological transition between two MBL phases. Through a Clifford-circuit based renormalisation group approach, we identify many-body resonances in the basis of localised eigenstates, showing that these proliferate in the vicinity of the transition and cause delocalisation. Additionally, we characterise the SPT strong zero mode. This has important implications for the stability of MBL and transitions between MBL phases with different topological orders.

(date/time/location: 27.02.2023, 11:30, Erwin Schrödinger lecture room, Boltzmanngasse 5, 5th floor, room 3500)