About

Michael Levin is a professor in the Department of Physics, the James Franck Institute, and the College at The University of Chicago. His research focuses on two main areas within quantum condensed matter physics. The first area involves the study of topological phases of matter, such as quantum Hall liquids and topological insulators. These phases are characterized by a rich internal structure that is topological in nature, unlike conventional phases like magnets or superconductors, which are associated with symmetry breaking or order parameters. Levin's work is dedicated to developing new concepts and tools to understand these systems. The second area of his research intersects quantum information theory and condensed matter physics. It addresses fundamental problems such as determining which quantum many-body systems can be efficiently simulated on a classical computer and developing methods to achieve this. This research has practical implications and is closely related to conceptual questions about the nature of entanglement in many-body ground states and the classification of gapped quantum phases of matter.

Research topics

• Computer Science
• Physics
• Theoretical physics
• Quantum mechanics
• Mathematics
• Geometry
• Literature
• Art
• Theoretical computer science
• Mathematical physics

Selected publications

• Topological constraints on self-organization in locally interacting systems

  Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 2026-05-14

  preprintOpen accessSenior author

  All intelligence is collective intelligence, in the sense that it is made of parts that must align with respect to system-level goals. Understanding the dynamics that facilitate or limit navigation of problem spaces by aligned parts thus impacts many fields ranging across life sciences and engineering. To that end, consider a system on the vertices of a planar graph, with pairwise interactions prescribed by the edges of the graph. Such systems can sometimes exhibit long-range order, distinguishing one phase of macroscopic behaviour from another. In networks of interacting systems, we may view spontaneous ordering as a form of self-organization, modelling neural and basal forms of cognition. Here, we discuss necessary conditions on the topology of the graph for an ordered phase to exist, with an eye towards finding constraints on the ability of a system with local interactions to maintain an ordered target state. By studying the scaling of free energy under the formation of domain walls in three model systems-the Potts model, autoregressive models and hierarchical networks-we show how the combinatorics of interactions on a graph prevent or allow spontaneous ordering. As an application, we are able to analyse why multiscale systems like those prevalent in biology are capable of organizing into complex patterns, whereas rudimentary language models are challenged by long sequences of outputs. This article is part of the theme issue 'World models in natural and artificial intelligence'.

  PublisherDOI

• Practitioners’ perceptions of biodiversity-relevant criteria for solar suitability analyses in the United States

  Research Square · 2025-09-26

  preprintOpen access
  PublisherOA PDFDOI

• Single Element Millimeter Wave Radar for Pedestrian Imaging

  2025-05-01

  report1st authorCorresponding
  PublisherDOI

• Many-Body Systems with Spurious Modular Commutators

  Physical Review Letters · 2024-12-20 · 4 citations

  articleSenior author

  Recently, it was proposed that the chiral central charge of a gapped, two-dimensional quantum many-body system is proportional to a bulk ground state entanglement measure known as the modular commutator. While there is significant evidence to support this relation, we show in this Letter that it is not universal. We give examples of lattice systems that have vanishing chiral central charge, which nevertheless give nonzero "spurious" values for the modular commutator for arbitrarily large system sizes, in both one and two dimensions. Our examples are based on cluster states and utilize the fact that they can generate nonlocal modular Hamiltonians.

  PublisherDOI

• Stability of topological superconducting qubits with number conservation

  Physical review. B./Physical review. B · 2024-04-01 · 2 citations

  articleSenior author

  The study of topological superconductivity is largely based on the analysis of simple mean-field models that do not conserve particle number. A major open question in the field is whether the remarkable properties of these mean-field models persist in more realistic models with a conserved total particle number and long-range interactions. For applications to quantum computation, two key properties that one would like to verify in more realistic models are (i) the existence of a set of low-energy states (the qubit states) that are separated from the rest of the spectrum by a finite energy gap, and (ii) an exponentially small (in system size) bound on the splitting of the energies of the qubit states. It is well known that these properties hold for mean-field models, but so far only property (i) has been verified in a number-conserving model. In this work we fill this gap by rigorously establishing both properties (i) and (ii) for a number-conserving toy model of two topological superconducting wires coupled to a single bulk superconductor. Our result holds in a broad region of the parameter space of this model, suggesting that properties (i) and (ii) are robust properties of number-conserving models and not just artifacts of the mean-field approximation.

  PublisherDOI

• Physical proof of the topological entanglement entropy inequality

  arXiv (Cornell University) · 2024-08-08

  preprintOpen access1st authorCorresponding

  Recently it was shown that the topological entanglement entropy (TEE) of a two-dimensional gapped ground state obeys the universal inequality $γ\geq \log \mathcal{D}$, where $γ$ is the TEE and $\mathcal{D}$ is the total quantum dimension of all anyon excitations, $\mathcal{D} = \sqrt{\sum_a d_a^2}$. Here we present an alternative, more direct proof of this inequality. Our proof uses only the strong subadditivity property of the von Neumann entropy together with a few physical assumptions about the ground state density operator. Our derivation naturally generalizes to a variety of systems, including spatially inhomogeneous systems with defects and boundaries, higher dimensional systems, and mixed states.

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• Physical proof of the topological entanglement entropy inequality

  Physical review. B./Physical review. B · 2024-10-22 · 4 citations

  article1st authorCorresponding

  It is generally believed that two-dimensional gapped phases of matter with anyon excitations have a special pattern of entanglement in their ground-state wave function. Recently, this intuition was formalized by a universal inequality relating the topological entanglement entropy of a gapped ground state to the total quantum dimension of its anyon excitations. This paper presents an alternative, more direct proof of this inequality.

  PublisherDOI

• Stability of ground state degeneracy to long-range interactions

  Journal of Statistical Mechanics Theory and Experiment · 2023-01-01 · 4 citations

  articleOpen accessSenior authorCorresponding

  Abstract We show that some gapped quantum many-body systems have a ground state degeneracy that is stable to long-range (e.g. power-law) perturbations, in the sense that any ground state energy splitting induced by such perturbations is exponentially small in the system size. More specifically, we consider an Ising symmetry-breaking Hamiltonian with several exactly degenerate ground states and an energy gap, and we then perturb the system with Ising symmetric long-range interactions. For these models we prove (a) the stability of the gap, and (b) that the residual splitting of the low-energy states below the gap is exponentially small in the system size. Our proof relies on a convergent polymer expansion that is adapted to handle the long-range interactions in our model. We also discuss applications of our result to several models of physical interest, including the Kitaev p-wave wire model perturbed by power-law density–density interactions with an exponent greater than 1.

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• Universal lower bound on topological entanglement entropy

  PubMed · 2023-02-01 · 1 citations

  preprintOpen access

  Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that characterizes the underlying topological phase. However, the TEE is not truly universal: it can differ even for two states related by constant-depth circuits, which are necessarily in the same phase. The difference between the TEE and the value predicted by the anyon theory is often called the "spurious" topological entanglement entropy. We show that this spurious contribution is always non-negative, thus the value predicted by the anyon theory provides a universal lower bound. This observation also leads to a definition of TEE that is invariant under constant-depth quantum circuits.

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• Exactly Solvable Model for a Deconfined Quantum Critical Point in 1D

  Physical Review Letters · 2023 · 43 citations

  Senior authorCorresponding
  • Physics
  • Mathematical physics
  • Quantum mechanics

  We construct an exactly solvable lattice model for a deconfined quantum critical point (DQCP) in (1+1) dimensions. This DQCP occurs in an unusual setting, namely, at the edge of a (2+1) dimensional bosonic symmetry protected topological (SPT) phase with Z_{2}×Z_{2} symmetry. The DQCP describes a transition between two gapped edges that break different Z_{2} subgroups of the full Z_{2}×Z_{2} symmetry. Our construction is based on an exact mapping between the SPT edge theory and a Z_{4} spin chain. This mapping reveals that DQCPs in this system are directly related to ordinary Z_{4} symmetry breaking critical points.

  PublisherDOI

Recent grants

• CAREER: Bulk and boundary properties of topological matter

  NSF · $465k · 2013–2018

Frequent coauthors

• Xiao-Gang Wen

  Massachusetts Institute of Technology

  11 shared

• Ady Stern

  10 shared

• Chenjie Wang

  9 shared

• T. Senthil

  Massachusetts Institute of Technology

  8 shared

• Erez Berg

  7 shared

• Sriram Ganeshan

  7 shared

• Mark S. Rudner

  University of Washington

  7 shared

• Zheng‐Cheng Gu

  Chinese University of Hong Kong

  7 shared

Awards & honors

• Simons Foundation Award (2019)