Sergej Moroz

Quantum Fluids

Technical University of Munich

TUM School of Natural Sciences

James-Franck-Str. 1

85747 Garching

Tel. +49 89 289 12884


Research Webpage

As a rule, quantum collective behavior of a macroscopic ensemble of particles is very different from the physics of its elementary constituents. The richness and universality of the emergent physical theories inspires and fuels my research of quantum phases of matter.


Research focus: topological phases in condensed matter, quantum fluids, universal few-body quantum physics

The main areas of research conducted in our group are concentrated around two broad topics: effective field theories of quantum phases of matter and discrete lattice gauge theories interacting with fermionic matter.

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 and geometry in quantum phases of matter. We develop effective theories of various low-dimensional many-body topological quantum fluids and crystals such as topological superfluids and superconductors, vortex crystals and quantum Hall fluids.

Selected Publications

  • Bosonic superfluid on lowest Landau level. Sergej Moroz, Dam Thanh Son, Phys. Rev. Lett. 122, 235301 (2019), [arXiv:1901.06088]
  • Effective field theory of a vortex lattice in a bosonic superfluid. Sergej Moroz, Carlos Hoyos, Claudio Benzoni, Dam Thanh Son, SciPost Phys. 5, 039 (2018), [arXiv:1803.10934]
  • Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors. Sergej Moroz, Abhinav Prem, Victor Gurarie, Leo Radzihovsky, Phys. Rev. B 95, 014508 (2017), [arXiv:1606.03462]
  • Effective theory of chiral two-dimensional superfluids. Carlos Hoyos, Sergej Moroz, Dam Thanh Son, Phys. Rev. B 89, 174507 (2014), [arXiv:1305.3925]

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.

Selected Publications

  • Confined phases of one-dimensional spinless fermions coupled to Z2 gauge theory. Umberto Borla, Ruben Verresen, Fabian Grusdt, Sergej Moroz, [arXiv:1909.07399]


Rayleigh edge waves in two-dimensional crystals with Lorentz forces: From skyrmion crystals to gyroscopic media

C. Benzoni, B. Jeevanesan, S. Moroz

Physical Review B 104, 024435 (2021).

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We investigate, within the framework of linear elasticity theory, edge Rayleigh waves of a two-dimensional elastic solid with broken time-reversal and parity symmetries due to a Berry term. As our prime example, we study the elastic edge wave traveling along the boundary of a two-dimensional skyrmion lattice hosted inside a thin-film chiral magnet. We find that the direction of propagation of the Rayleigh modes is determined not only by the chirality of the thin film, but also by the Poisson ratio of the crystal. We discover three qualitatively different regions distinguished by the chirality of the low-frequency edge waves, and study their properties. To illustrate the Rayleigh edge waves in real time, we have carried out finite-difference simulations of the model. Apart from skyrmion crystals, our results are also applicable to edge waves of gyroelastic media and screened Wigner crystals in magnetic fields. Our work opens a pathway towards controlled manipulation of elastic signals along boundaries of crystals with broken time-reversal symmetry.

DOI: 10.1103/PhysRevB.104.024435

Gauging the Kitaev chain

U. Borla, R. Verresen, J. Shah, S. Moroz

Scipost Physics 10 (6), 148 (2021).

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We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.

DOI: 10.21468/SciPostPhys.10.6.148

Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

D.X. Nguyen, A. Gromov, S. Moroz

Scipost Physics 9 (5), 076 (2020).

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Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

DOI: 10.21468/SciPostPhys.9.5.076

Thermodynamics of two-dimensional bosons in the lowest Landau level

B. Jeevanesan, S. Moroz.

Physics Review Research 2, 33323 (2020).

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We study the thermodynamics of short-range-interacting, two-dimensional bosons constrained to the lowest Landau level. When the temperature is higher than other energy scales of the problem, the partition function reduces to a multidimensional complex integral that can be handled by classical Monte Carlo techniques. This approach takes the quantization of the lowest Landau level orbits fully into account. We observe that the partition function can be expressed in terms of a function of a single combination of thermodynamic variables, which allows us to derive exact thermodynamic relations. We determine the asymptotic behavior of this function and compute some thermodynamic observables numerically.

DOI: 10.1103/PhysRevResearch.2.033323

Hall viscosity and conductivity of two-dimensional chiral superconductors

F. Rose, O. Golan, S. Moroz

Scipost Physics 9 (1), 006 (2020).

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We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chi-ral superconductors, where fermions pair due to a short-range attractive potential, e.g. p + ip pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chiral superconductors, where the Coulomb potential decays as inverse distance, we find an intermediate behavior between intrinsic two-dimensional superconductors and superfluids. These results are obtained by means of both effective and microscopic field theory.

DOI: 10.21468/SciPostPhys.9.1.006

Confined Phases of One-Dimensional Spinless Fermions Coupled to Z(2) Gauge Theory

U. Borla, R. Verresen, F. Grusdt, S. Moroz

Physical Review Letters 124 (12), 120503 (2020).

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We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z(2) gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.

DOI: 10.1103/PhysRevLett.124.120503

Boundary central charge from bulk odd viscosity: Chiral superfluids

O. Golan, C. Hoyos, S. Moroz

Physical Review B 100 (10), 104512 (2019).

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We derive a low-energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave vector, contains a dependence on the chiral central charge c of the boundary degrees of freedom, as well as additional nonuniversal contributions. We identify related bulk observables which allow for a bulk measurement of c. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model.

DOI: 10.1103/PhysRevB.100.104512

Helical spin texture in a thin film of superfluid 3He

T. Brauner, S. Moroz

Physical Review B 99, 214506 (2019).

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We consider a thin film of superfluid 3He under conditions that stabilize the A phase. We show that in the presence of a uniform superflow and an external magnetic field perpendicular to the film, the spin degrees of freedom develop a nonuniform, helical texture. Our prediction is robust and relies solely on Galilei invariance and other symmetries of 3He, which induce a coupling of the orbital and spin degrees of freedom. The length scale of the helical order can be tuned by varying the velocity of the superflow and the magnetic field and may be in reach of near-future experiments.

DOI: 10.1103/PhysRevB.99.214506

Bosonic superfluid on lowest Landau level

S. Moroz, D. T. Son.

Physic Review Letters 122, 235301 (2019).

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We develop a low-energy effective field theory of a two-dimensional bosonic superfluid on the lowest Landau level at zero temperature and identify a Berry term that governs the dynamics of coarse-grained superfluid degrees of freedom. For an infinite vortex crystal we compute how the Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations and non-dissipative Hall responses of the particle number current and stress tensor. This term gives rise to a quadratic in momentum term in the Hall conductivity, but does not generate a non-dissipative Hall viscosity.

DOI: 10.1103/PhysRevLett.122.235301

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