# Research

## Effective theories in

## condensed matter physics

Although microscopically condensed matter physics is about interaction between electrons, protons, neutrons and light, often the many-body nature of the problem gives rise to 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 set-up 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.

- Effective theory of chiral two-dimensional superfluids, Phys. Rev. B **89**, 174507 (2014), [arXiv:1305.3925]

-Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation, Phys. Rev. B **91**, 064508 (2015), [arXiv:1408.5911]

-Effective field theory of a vortex lattice in a bosonic superfluid, SciPost **5**, 039 (2018), [arXiv:1803.10934]

-Bosonic superfluid on lowest Landau level, Phys. Rev. Lett. **122**, 235301 (2019), [arXiv:1901.06088]

## Discrete lattice gauge theories interacting with fermionic matter

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 Z2 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. Since the Ising gauge field mediates attraction, when coupled to fermionic matter it leads to formation of an exotic superfluid state. In our group we use analytical methods and numerical density matrix renormalization group (DMRG) approach to understand quantum phases of fermions coupled to the Ising gauge theory in one and two spatial dimensions. 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.

-Confined phases of one-dimensional spinless fermions coupled to Z2 gauge theory, Phys. Rev. Lett. **124**, 120503 (2020) [arXiv:1909.07399]

## Topological order

## in superconductors

The discovery of superconductivity is a milestone of 20th century physics. Based on the Cooper pairing mechanism of electrons, the microscopic BCS theory of superconductivity is very successful in making sense of a large class of phenomena that are exhibited by superconductors. At energies much below the superconducting gap, however, a new description of a superconductor should emerge. In this low-energy world, what actually matters is only how the low-energy excitations of a superconductor- Bogoliubov quasiparticles and vortices- braid and fuse with each other and what symmetry quantum numbers they have. The BCS description of superconductors relies on spontaneous symmetry breaking of the particle number symmetry. If one, however, takes into account fluctuations of the electromagnetic photons, the particle number symmetry is gauged and cannot be spontaneously broken. Similar to quantum Hall fluids and spin liquids, superconductors exhibit new kind of order, known as a topological order, manifested in the fractionalization of low-energy excitations, ground state degeneracy on closed manifolds, and long-range entanglement. In our group we develop topological field theories of fully gapped superconductors that naturally incorporate topological order and take into account global symmetries of superconductors. By merging topological order with symmetries, whose interplay is one of the most vibrant avenues in modern condensed matter physics, we put superconductors into the class of symmetry enriched topological (SET) phases of matter.

- Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors, Phys. Rev. B **95**, 014508 (2017), [arXiv:1606.03462]

- Screening and Topological Order in Thin Superconducting Films, New J. Phys. **20**, 083049 (2018), [arXiv:1706.01310]

## Weyl nodal surfaces

The advent of topological insulators in the last decade deepened our understanding of interplay of topology and symmetries in band insulators. This work culminated in the development of the ten-fold way classification of non-interacting gapped topological phases and the emergence of new symmetry protected topological phases of matter. In last years the main interest in the field shifted towards systems with band degeneracies. In three dimensions the simplest and most well-studied are Weyl (semi)metals which are distinguished by isolated pointlike two-band degeneracies in the Brillouin zone. In our group we are interested in Weyl nodal surfaces where two bands touch each other on two-dimensional surfaces in the Brillouin zone. This is a theoretical frontier of research of nodal structures in band theory with a lot of exciting unanswered questions.

- Weyl nodal surfaces,* *Phys. Rev. B **97**, 075120 (2018), [arXiv:1709.01561]

- Coulomb-induced instabilities of nodal surfaces, Phys. Rev. B **98**, 241107(R) (2018),* * [arXiv:1807.09170]

## Universality

## in few-body quantum physics

In quantum mechanics three identical bosons in three dimensions interacting resonantly via a short-range two-body potential form an infinite tower of Borromean bound states, whose energy spectrum organizes itself into a geometric series accumulating at zero energy. This was discovered theoretically by Vitaly Efimov in 1970 and is known today as the Efimov effect. This effect is a beautiful example of few-body universality since it is independent of the detailed form of the interaction potential provided it is tuned to the resonance. Last decade saw a wave of interest in few-body Efimov physics which was fueled by its experimental verification in cold atom experiments. Although originally predicted to occur only in three-dimensional systems with short-range resonant interactions, the Efimov physics is more general. In our group we are pushing forward the theoretical frontier of the Efimov physics focusing mainly to lower-dimensional systems.

- Super Efimov effect of resonantly interacting fermions in two dimensions,* *Phys. Rev. Lett. **110**, 235301 (2013), [arXiv:1301.4473]

- Generalized Efimov effect in one dimension,* *Phys. Rev. Lett. **115**, 180406 (2015), [arXiv:1506.03856]