Research

Gauge theories play a central role in our current description of Nature. During the last century, gauge invariance proved to be a valuable guiding principle in physics, to the point that all the known fundamental interactions in particle physics beyond electromagnetism are now described by some non-Abelian Yang-Mills gauge theories. Lattice regularization is widely used in high energy physics to study strongly coupled quantum gauge theories. Lattice gauge theories also arise naturally in the context of nowadays condensed matter physics in lattice problems where low-energy excitations fractionalize. 

Theoretical discovery of the Ising Z_2 gauge theory led to a drastic shift of paradigm of our understanding of phase transitions and was the first example of a system that exhibits topological order. In our group, we use analytical and numerical methods to shed new light on different phases of quantum matter coupled to the Ising gauge theory in one and two spatial dimensions. We are also interested in phenomenology of quantum dynamics in discrete gauge theories. Our research is partially motivated by recent advances in cold atom experiments, where prototypes of the Ising gauge theory coupled to matter are actively studied.

Recently, we extended our research to lattice gauge theories beyond Z_2.

Papers:

-Confined phases of one-dimensional spinless fermions coupled to Z_2 gauge theory,  [arXiv:1909.07399] 

-Gauging the Kitaev chain, SciPost 10, 148 (2021) [arXiv:2010.00607] 

-Quantum phases of two-dimensional Z_2 gauge theory coupled to single-component fermion matter, [arXiv:2012.08543] 

-Fractionalized holes in one-dimensional Z_2 gauge theory coupled to fermion matter -- deconfined dynamics and emergent integrability,  [arxiv:2111.13205] 

-Confinement Induced Frustration in a One-Dimensional Z_2 Lattice Gauge Theory, [arxiv:2206.13487] 

-Finding the ground state of a lattice gauge theory with fermionic tensor networks: a 2+1d Z_2 demonstration, [arxiv:2211.00023] 

-Higgs Condensates are Symmetry-Protected Topological Phases: I. Discrete Symmetries [arxiv:2211.01376] 

-Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids [arxiv:2306.09405 ]

-In pursuit of deconfined quantum criticality in Ising gauge theory entangled with single-component fermions [arxiv: 2402.00933]

-Higgs Phases and Boundary Criticality [arxiv:2404.17001 ]

Although microscopically condensed matter physics is about the interaction between electrons, protons, neutrons and light, often the many-body nature of the problem gives rise to the emergence of new degrees of freedom with intriguing collective behavior at low energies. These degrees of freedom constitute the building blocks of effective field theories that in addition are constrained by symmetries of the problem. This setup provides a reliable micro-independent framework for non-perturbative understanding of strongly interacting quantum systems. In our group, we are especially interested in the interplay of topology, symmetry and geometry in quantum phases of matter. We develop and apply effective theories for various quantum fluids and solids in superfluids, superconductors and quantum Hall states.

Papers:

- Effective theory of chiral two-dimensional superfluids, [arXiv:1305.3925] 

-Effective field theory of a vortex lattice in a bosonic superfluid, [arXiv:1803.10934]

-Bosonic superfluid on lowest Landau level, [arXiv:1901.06088]

-Hall viscosity and conductivity of two-dimensional chiral superconductors, [arXiv:2004.02590]

-Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting, [arXiv:2005.12317]

-Rayleigh Edge Waves in Two-Dimensional Crystals with Lorentz Forces -- from Skyrmion Crystals to Gyroscopic Media, [arXiv:2004.09517] 

-Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate, [arXiv:2212.08671] 

-On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity, [arxiv: 2310.13741]

Over the past decade, our understanding of symmetries has significantly evolved, providing deep new insights into what constitutes a symmetry and how it constrains physical observables. This modern approach has unified various aspects of complex physical systems, leading to new concepts such as higher-form, higher-group, non-invertible, and multipole symmetries . These rapid developments also led to deeper thinking about anomalies and general constraints that follow from them. In our group we investigate emergence of generalized symmetries in condensed matter many-body quantum systems.

Papers:

-Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting, [arXiv:2005.12317]

-Higgs Condensates are Symmetry-Protected Topological Phases: I. Discrete Symmetries [arxiv:2211.01376] 

-Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate, [arXiv:2212.08671] 

-On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity, [arxiv: 2310.13741]

- The Ising dual-reflection interface: ℤ4 symmetry, Majorana strong zero modes and SPT phases,  [2412.06377]