Research
Our group works at the interface of computational and theoretical condensed matter physics, with a sustained focus on topological phases of matter, frustrated quantum magnetism, and — increasingly — the statistical mechanics of quantum information.
A long-standing theme has been the search for emergent gauge structure and fractionalization in correlated systems. This has taken us from interacting non-Abelian anyon chains to the rich landscape of Kitaev materials, where we have explored two- and three-dimensional spin liquids, field-driven phases, and the connection between solvable models and real honeycomb iridates and ruthenates. In parallel, our work on frustrated magnetism — using pseudo-fermion functional renormalization group techniques alongside other numerical methods — addresses quantum spin liquids and unconventional orders on pyrochlore, kagome, maple-leaf, and moiré lattices
More recently, our interests have expanded toward the physics of monitored quantum systems and quantum error correction. We study measurement-induced phase transitions, learning transitions in topological codes, and the emergence of Nishimori universality in decohered and weakly measured quantum states — topics that bring together disordered statistical mechanics, replica field theory, and the practical concerns of near-term quantum hardware.
Underlying all of this is a methodological commitment that has shaped the group since its inception: developing and refining the computational tools — Monte Carlo, tensor networks, functional renormalization group, machine learning — that make these questions tractable.
Measurement-induced phase transitions and quantum information
A central focus of our current research concerns the dynamics of quantum many-body systems subject to measurement and decoherence. We study how repeated measurements in weakly monitored quantum circuits drive entanglement transitions, how decoherence reshapes topologically ordered states, and how the resulting phase structure is captured by replica field theories and disordered statistical-mechanics models – often along the Nishimori line. A recurring theme is the stabilization of long-range entanglement from finite-depth unitaries and weak measurements, and more recently the higher Nishimori criticality that governs learning transitions in deformed toric codes. This program connects fundamental questions about the quantum-to-classical boundary with practical concerns about error correction in near-term quantum devices.
Quantum error correction and topological codes
Closely related to our work on monitored systems is a growing program on quantum error correction. We study learning transitions and error thresholds in toric and surface codes, robust teleportation protocols and the cascade of topological transitions they induce, Floquet codes and their connection to emergent Majorana physics, and scalable neural decoders for topological surface codes. A recent collaboration with IBM demonstrated the Nishimori transition on a superconducting quantum processor – bringing decades of theoretical work on disordered statistical mechanics into direct contact with quantum hardware.
Frustrated quantum magnetism
Geometric frustration provides a fertile route to unconventional ground states, from quantum spin liquids to noncoplanar magnetic orders. We investigate frustrated magnets on a wide range of lattice geometries – kagome, pyrochlore, maple-leaf, square-kagome, diamond, and triangular moiré structures – combining numerical, analytical, and field-theoretical approaches. Particular attention is paid to higher-rank U(1) spin liquids on pyrochlore lattices, pinch-point and half-moon signatures in neutron scattering, the noncoplanar orders and quantum-disordered states of maple-leaf antiferromagnets, and the quantum spin liquids realized in spin-1 diamond antiferromagnets.
Spectroscopy of quantum magnets
In collaboration with experimental groups, we study how non-trivial excitations of quantum magnets – spinons, multipolar modes, bound states, and confinement signatures – manifest in spectroscopic probes. Recent work has focused on two-dimensional coherent spectroscopy as a new tool to disentangle these excitations, with applications ranging from quadrupolar excitations revealed by non-linear spectroscopy to the spectroscopic fingerprints of CoNb2O6. In parallel, resonant inelastic X-ray scattering reveals bond-directional excitations and other fingerprints of Kitaev physics in the honeycomb iridates. This thread connects our theoretical work on spin liquids and frustrated magnets to direct experimental observables.
Kitaev materials and spin liquids
Kitaev's exactly solvable honeycomb model has motivated an extensive search for material realizations and generalizations, surveyed in our Kitaev Materials review. Our group has contributed to both ends of this program: the systematic classification of gapless Z2 spin liquids on three-dimensional lattices – including Majorana Fermi surfaces, Weyl spin liquids, and higher-order topological variants – and the study of candidate materials, beginning with the recognition that the Heisenberg-Kitaev model is relevant to the honeycomb iridates A2IrO3. We have since explored the emergence of a field-driven U(1) spin liquid in the Kitaev honeycomb model and helped interpret the half-integer quantized thermal Hall effect observed in the Kitaev material candidate α-RuCl3.
Machine learning for quantum matter
Machine learning techniques offer new perspectives on long-standing problems in condensed matter. Our group has developed both unsupervised and supervised approaches to phase recognition, including methods that work in the presence of the fermion sign problem, as well as scalable neural decoders for topological surface codes and reinforcement-learning environments for quantum control. Related techniques such as quantum loop topography have helped identify non-Fermi liquid physics in quantum critical metals. These efforts sit at the intersection of statistical learning theory and quantum many-body physics.
Quantum critical metals and sign-problem-free Monte Carlo
A series of works in collaboration with experimental and theoretical partners has used determinantal quantum Monte Carlo to study metallic quantum critical points – in particular the spin-density-wave transition in two-dimensional metals and the hierarchy of energy scales near an antiferromagnetic critical point. By exploiting sign-problem-free formulations, these simulations provide unbiased benchmarks for how non-Fermi liquid behavior and competing orders such as superconductivity emerge near quantum criticality.
Interacting non-Abelian anyons
A foundational interest of the group has been the collective behavior of interacting anyons – exotic quasiparticles that obey neither bosonic nor fermionic statistics. Starting with the "golden chain" of interacting Fibonacci anyons, we have explored how non-Abelian anyons form one-dimensional quantum liquids, drive topology-driven quantum phase transitions, and – in the presence of disorder – condense into a disorder-induced Majorana metal. This line of work also connects to the chiral spin liquid and emergent anyons realized in a kagome-lattice Mott insulator, establishing interacting anyon models as a microscopic playground for topological quantum criticality.
Optimized statistical ensembles and open source codes
A sustained interest of the group, dating to its earliest years, lies in the numerical methods themselves. We introduced a scheme for optimizing the statistical ensemble in broad-histogram Monte Carlo simulations, demonstrated the performance limitations of flat-histogram methods, and developed feedback-optimized parallel tempering – techniques now used well beyond condensed matter, and reviewed in our lecture notes on ensemble optimization. Much of this was made publicly available through the ALPS project, our open-source framework for strongly correlated systems. This methodological strand continues to inform our current work on quantum Monte Carlo, tensor networks, and the simulation of monitored quantum circuits.