pollmann

Theoretical Solid State Physics

Technical University of Munich

TUM School of Natural Sciences

James-Franck-Straße 1

85748 Garching

+49 89 289 53760

frank.pollmann[at]tum.de

Research Website

We seek to understand how fascinating physical phenomena like superconductivity, magnetism, and topological order can emerge from simple interactions between many microscopic quantum particles.

Description

Research focus: topological phases of matter, quantum many-body entanglement, solid state theory

Matter occurs in various phases with different properties. For example, certain solids become magnetic when cooled to sufficiently low temperatures, and others become superconductors, i.e., they conduct electrical current without dissipation. Both of these phases are examples of collective phenomena, which arise due to the interactions between many electrons in the solid. Our group is interested in systems where the interaction between the electrons yields new phases of matter.


One focus is the investigation of topological phases—which are prime examples of exotic phases with unusual properties. Intriguingly, such phases may be ideal building blocks of fault-tolerant quantum computers. Topological phases are very different from conventional phases of matter and have no classical analogue. They are characterized by their low-energy anyonic excitations, which are highly non-local objects that can sense each other through the medium in which they live even when they are very far apart. In our studies, we develop conceptual frameworks for classifying topological phases and we construct concrete models in order to realize them as a first step towards searching for these phases in nature.

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We are also interested in understanding quantum many-body systems far out of equilibrium. Historically, the non-equilibrium evolution of quantum states was limited to extremely short time spans because of dissipation and decoherence effects. Recent experiments on ultra-cold gases in optical lattices as well as in nano structures allowed for the first time to overcome these limitations. At the same time, there has been a huge advance in the development of numerical and analytical techniques, which allow us to get a deeper understanding of the experiments. In particular, highly efficient numerical methods based on matrix-product states allow a direct comparison with theoretical predictions and experimental results.

Publications

Scalable simulation of nonequilibrium quantum dynamics via classically optimized unitary circuits

L. Causer, F. Jung, A. Mitra, F. Pollmann, A. Gammon-Smith

Physical Review Research 6 (3), 33062 (2024).

Show Abstract

The advent of near-term digital quantum computers could offer us an exciting opportunity to investigate quantum many-body phenomena beyond that of classical computing. To make the best use of the hardware available, it is paramount that we have methods that accurately simulate Hamiltonian dynamics for limited circuit depths. In this paper, we propose a method to classically optimize unitary brickwall circuits to approximate quantum time evolution operators. Our method is scalable in system size through the use of tensor networks. We demonstrate that, for various three-body Hamiltonians, our approach produces quantum circuits that can outperform trotterization in both their accuracy and the quantum circuit depth needed to implement the dynamics, with the exact details being dependent on the Hamiltonian. We also explain how to choose an optimal time step that minimizes the combined errors of the quantum device and the brickwall circuit approximation.

DOI: 10.1103/PhysRevResearch.6.033062

Ballistic to diffusive crossover in a weakly interacting Fermi gas

J. Lloyd, T. Rakovszky, F. Pollmann, C. von Keyserlingk

Physical Review B 109 (20), 205108 (2024).

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In the absence of disorder and interactions, fermions move coherently and their associated charge and energy exhibit ballistic spreading, even at finite energy density. In the presence of weak interactions and a finite energy density, fermion-fermion scattering leads to a crossover between early-time ballistic and late-time diffusive transport. The relevant crossover timescales and the transport coefficients are both functions of interaction strength, but the question of determining the precise functional dependence is likely impossible to answer exactly. In this work we develop a numerical method (fDAOE) which is powerful enough to provide an approximate answer to this question, and which is consistent with perturbative arguments in the limit of very weak interactions. Our algorithm, which adapts the existing dissipation-assisted operator evolution (DAOE) to fermions, is applicable to systems of interacting fermions at high temperatures. The algorithm approximates the exact dynamics by systematically discarding information from high n-point functions, and is tailored to capture noninteracting dynamics exactly. Applying our method to a microscopic model of interacting fermions, we numerically determine crossover timescales and diffusion constants for a wide range of interaction strengths. In the limit of weak interaction strength (A), we demonstrate that the crossover from ballistic to diffusive transport happens at a time tD similar to 1/A2 and that the diffusion constant similarly scales as D similar to 1/A2. We confirm that these scalings are consistent with a perturbative Fermi's golden rule calculation, and we provide a heuristic operator-spreading picture for the crossover between ballistic and diffusive transport.

DOI: 10.1103/PhysRevB.109.205108

Topological phases in the dynamics of the simple exclusion process

J. P. Garrahan, F. Pollmann

Physical Review E 109 (3), L032105 (2024).

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We study the dynamical large deviations of the classical stochastic symmetric simple exclusion process (SSEP) by means of numerical matrix product states. We show that for half filling, long-time trajectories with a large enough imbalance between the number hops in even and odd bonds of the lattice belong to distinct symmetryprotected topological (SPT) phases. Using tensor network techniques, we obtain the large deviation (LD) phase diagram in terms of counting fields conjugate to the dynamical activity and the total hop imbalance. We show the existence of high activity trivial and nontrivial SPT phases (classified according to string order parameters) separated by either a critical phase or a critical point. Using the leading eigenstate of the tilted generator, obtained from infinite-system density-matrix renormalization group simulations, we construct a near-optimal dynamics for sampling the LDs, and show that the SPT phases manifest at the level of rare stochastic trajectories. We also show how to extend these results to other filling fractions, and discuss generalizations to asymmetric SEPs.

DOI: 10.1103/PhysRevE.109.L032105

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