Research

Transverse Quantum Fluids

Even when ideal solids are insulating, their states with crystallographic defects may have superfluid properties. It became clear recently that edge dislocations in 4He featuring a combination of microscopic quantum roughness and superfluidity of their cores may represent a new paradigmatic class of quasi-one-dimensional superfluids. The new state of matter, termed transverse quantum fluid (TQF), is found in a variety of physical setups [1-6]. The key ingredient defining the class of TQF systems is infinite compressibility, which is responsible for all other unusual properties such as the quadratic spectrum (or even the absence) of normal modes, irrelevance of the Landau criterion, off-diagonal long-range order at T = 0, and the exponential dependence of the phase slip probability on the inverse flow velocity. From a conceptual point of view, the TQF state is a striking demonstration of the conditional character of many dogmas associated with superfluidity, including the necessity of elementary excitations, in general, and the ones obeying Landau criterion in particular.

The possible realizations of TQF:

(A) A Bloch domain wall in an easy-axis ferromagnet

Right figure: Phase separated state of the hard-core bosonic Hamiltonian with nearest-neighbor attraction V < -2t at half-filling. It can be also viewed as the phase separated state of the easy-axis XY ferromagnet at zero total magnetization. For more information, see Ref. [4].

(B) A phase separated state of two-component bosonic insulators with the boundary in the counter superfluid phase (or in a phase of a two-component superfluid) on a 2D lattice

Right figure: Two-component bosons (red and blue circles) at unity filling in the regime of phase separation. Counter propagating motion by exchanging particles’ places of different types along the boundary results in the boundary motion in the transverse direction. For more information, see Ref. [4].

(C) A spectacular example of TQF-based physics: Quantum “hockey puck on sandpaper” moving without gliding and friction

The solid-on-solid friction was pondered about by Aristotle, Leonardo da Vinci and since then by many scientists and engineers but the exact nature of friction is still poorly understood. The consensus is that under no circumstances this type of friction can be eliminated or circumvented. We show that there is an exception from this more than 2000 years old dogma.  The system we call “quantum puck” can perform a novel type of quantum mechanical motion supported by superfluid state at its edges.  Despite that inside of the puck remains static, the superfluid edge currents, which are frictionless, transfer the matter in such a way that the entire puck appears moving. This effect can be experimentally implemented with either ultracold atoms in optical lattice—as a self-trapped insulating droplet, or within a crystal of 4He—as an edge dislocation loop. Persistent supercurrent along the edge dramatically changes puck’s dynamics: it now resembles that of a charged two-dimensional particle in a perpendicular magnetic field. In a uniform force field, the puck with the supercurrent demonstrates a spectacular gyroscopic effect—uniform motion in the perpendicular to the force direction.

Right figure: Insulating domain with 1260 particles at V = -2.2t (symbol sizes are proportional to the average occupation number). Simulations were performed at temperature T = t/128. The red line is a circle used for better visualization of the domain shape. By symmetry, a void in the insulator occupying the outer space has the same properties . For more information, see Ref. [5].

(D) A 1D bosonic liquid, Josephson coupled to a collection of transverse LLs

Incoherent transverse quantum fluids (iTQF) share with TQFs the existence of genuine off-diagonal long-range order (Bose-Einstein condensate) in the ground state, as well as the strong topological protection of supercurrent states due to the tight-binding of instantons. Nevertheless, iTQF is a different phase of matter: it lacks well-defined quasiparticles and features instead a diffusive dynamics of the field of superfluid velocity.

Right figure: Minimal iTQF model: Hard-core bosons at filling factor n = 0.5 on the square lattice, with all hopping amplitudes between sites in the x direction suppressed, except along the single row at y = 0. The nonzero hopping amplitudes are marked by solid lines. Inset: Image of a system of finite length with periodic boundary conditions, supporting a superflow along the central loop, which we expect to be implementable experimentally. For more information, see Ref. [6].

For a comprehensive review of these activities, see Ref. [7].

References:

  1. A. B. Kuklov, L. Pollet, N. V. Prokof’ev, and B. V. Svistunov, Supertransport by superclimbing dislocations in 4He: When all dimensions matter, Phys. Rev. Lett. 128, 255301 (2022).
  2. L. Radzihovsky, A. Kuklov, N. Prokof’ev, and B. Svistunov, Superfluid edge dislocation: Transverse quantum fluid, Phys. Rev. Lett. 131, 196001 (2023).
  3. A. Kuklov, N. Prokof’ev, L. Radzihovsky, and B. Svistunov, Transverse quantum fluids, Phys. Rev. B 109, L100502 (2024).
  4. C. Zhang, M. Boninsegni, A. Kuklov, N. Prokof’ev, and B. Svistunov, Superclimbing modes in transverse quantum fluids: Signature statistical and dynamical features, Phys. Rev. B 109, 214519 (2024).
  5. A. Kuklov, N. Prokof’ev, and B. Svistunov, Autonomous dynamics of two-dimensional insulating domain with superclimbing edge, Phys. Rev. Res. 6, 033008 (2024).
  6. A. Kuklov, L. Pollet, N. Prokof’ev, L. Radzihovsky, and B. Svistunov, Universal correlations as fingerprints of transverse quantum fluids, Phys. Rev. A 109, L011302 (2024).
  7. A. Kuklov, L. Pollet, N. Prokof’ev, and B. Svistunov, Transverse quantum Superfluids, arXiv: 2404.15480

Bi-polaron superconductivity in the low density limit

It has been assumed for decades that high values of Tc from electron-phonon coupling are impossible. At weak-to-intermediate coupling strength, this result follows from the Migdal-Eliashberg theory, while at strong coupling, when bipolarons form, the transition temperatures are low due to the large effective mass enhancement. However, this conclusion was based on numerical solutions of the Holstein model. We considered a different model with electron-phonon coupling based on the displacement-modulated hopping of electrons (the bond Peierls/Su-Schrieffer-Heeger electron-phonon coupling) and found that much larger values of the bipolaron Tc can be achieved in this setup. To begin with, polarons of the bond type were found to remain relatively light in the strong electron-phonon coupling limit [1]. Next, we develpped a new algorithm within the general path-integral Monte Carlo scheme for the particle sector, utilizing either the diagrammatic representation or Fock path-integral representation for the phonon sector to study the properties of bond/Holstein polarons/bipolarons [2]. The non-locality of the bond electron-phonon coupling gives rise to small-size, yet relatively light bipolarons, which can be studied by our method even in the presence of strong Hubbard and Coulomb potentials. To determine the transition temperature in the bipolaron model, we numerically calculated the superconducting transition temperature for the Coulomb Bose gas [3] and established an acurate framework for estimating Tc in the bipolaron gas. We found that for bond-type bipolarons Tc significantly exceeds typical upper bounds based on Migdal-Eliashberg theory or for Holstein bipolarons [4,5], thus offering a route towards the design of high- superconductors via functional material engineering.

Finally, we introduced an algorithm for solving a broad class of polaron problems with highly nonlinear electron-phonon coupling, which were previously considered unsolvable without uncontrolled simplifications. It works in the coordinate representation for both the particle and atomic displacements [6],  and was used to study polarons from quadratic electron-phonon interactions, including soliton states [7,8] .

References:

  1. Chao Zhang, Nikolay V. Prokof’ev, and Boris V. Svistunov, Peierls/Su-Schrieffer-Heeger Polarons in two dimensions, Phys. Rev. B 104, 035143 (2021)
  2. Chao Zhang, Nikolay V. Prokof’ev, and Boris V. Svistunov, Bond Bipolarons: Sign-free Monte Carlo Approach, Phys. Rev. B 105, L020501 (2022)
  3. Chao Zhang, Barbara Capogrosso-Sansone, Massimo Boninsegni, Nikolay V. Prokof’ev, and Boris V. Svistunov, Superconducting transition temperature of the Bose one-component plasma, Phys. Rev. Lett. 130, 236001 (2023)
  4. Chao Zhang, John Sous, David R. Reichman, Mona Berciu, Andrew J. Millis, Nikolay V. Prokof’ev, and Boris V. Svistunov, Bipolaronic high-temperature superconductivity, Phys. Rev. X 13, 011010 (2023)
  5. John Sous, Chao Zhang, Mona Berciu, David R. Reichman, Boris V. Svistunov, Nikolay V. Prokof’ev, and Andrew J. Millis, Bipolaronic superconductivity out of a Coulomb gas, Phys. Rev. B 108, L220502 (2023)
  6. Nikolay Prokof’ev and Boris Svistunov, Phonon modulated hopping polarons: x-representation technique, Phys. Rev. B 106, L04117 (2022)
  7. Zhongjin Zhang, Anatoly Kuklov, Nikolay Prokof’ev, and Boris Svistunov, Soliton states from quadratic electron-phonon interaction, Phys. Rev. B 108, 245127 (2023)
  8. Stefano Ragni, Thomas Hahn, Zhongjin Zhang, Nikolay Prokof’ev, Anatoly Kuklov, Serghei Klimin, Matthew Houtput, Boris Svistunov, Jacques Tempere, Naoto Nagaosa, Cesare Franchini, Andrey S Mishchenko, Polaron with quadratic electron-phonon interaction, Phys. Rev. B 107, L121109 (2023)

Related seminar talks: “Bi-polaron Superconductivity in the Low Density Limit” and “Bond polarons”.

Ultra-cold gases

Our group is interested in novel states of quantum matter, universal thermodynamic and dynamic properties of continuous phase transitions, ground-state and finite-temperature phase diagrams, as well as benchmark calculations of experimental systems. To deal with effects of strong correlations in bosonic and fermionic Hamiltonians we employ a combination of exact analytic considerations, path integral, and diagrammatic Monte Carlo methods. Some of the highlights include universal properties of weakly-interacting Bose gases in the fluctuation region, the BCS-BEC crossover curve for the resonant Fermi gas, quantum critical dynamics at the superfluid-to-Mott insulator phase transition, and ground-state phase diagrams for disordered bosons.

Fermi polaron

The Fermi polaron is an impurity interacting with a sea of fermions. Similar setups have been addressed in the context of electric conductance (electrons immersed in a bath of phonons — the collective excitations of the dielectric medium) or mixtures of different helium isotopes. In atomic physics the Fermi polaron can also be understood as the limiting case of a population-imbalanced two-species system, where one species has been diluted so strongly that it now merely consists of one particle. The impurity exchanges momentum with particles in the Fermi sea, thus creating particle-hole pairs. If interactions are sufficiently strong, a molecular bound state forms between the impurity and a fermion from the environment. Diagrammatic Monte Carlo has proven very successful in calculating different properties of the Fermi polaron. It allows us to study the system in a controlled, systematically improvable way and with great precision. Currently we study the polaron spectral function, which is directly linked to many of its physical propertis and is the quantity probed in experiments.

Frustrated Quantum Magnets

A characteristic feature of all frustrated magnets is close competition among numerous spin configurations and absence of an obvious arrangement that gains the maximum amount of energy from all interaction terms. Frustration prevents the development of long-range magnetic orders and often leads to novel and exotic collective phenomena. One of the best known examples is the fluid-like states of magnets, so-called spin liquids, in which the constituent spins are highly correlated but still fluctuate strongly down to a temperature of absolute zero. The fluctuations of the spins in a spin liquid can be classical or quantum and show remarkable collective phenomena such as emergent gauge fields and fractionalized excitations. Unfortunately, in the strongly correlated regime of frustrated spin systems, conventional Monte Carlo methods suffer from the notorious sign problem, and variational methods are not applicable. Our approach is to employ the Diagrammatic Monte Carlo (DiagMC) method, which is based on Monte Carlo sampling of skeleton Feynman diagrams, within the fermionization framework of spin systems. The DiagMC method allows us to study the low temperature physics of strongly correlated quantum spin systems in a controlled way. The first successful application of DiagMC to spin systems is the study of the triangular lattice spin-1/2 Heisenberg model. We reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures in the correlated paramagnet regime. We can also obtain the zero temperature physics by extrapolation of this relation. In our recent work, we performed a DiagMC study of the SU(2)-symmetric spin-1/2 Heisenberg antiferromagnet on a pyrochlore lattice and found a “fingerprint” evidence for the thermal spin-ice state in a broad low temperature regime where degenerate states satisfy the “2-in/2-out” ice rule on each tetrahedron. The dynamics of the fractional excitations has also been revealed.

Quantum Critical Dynamics

A quantum critical point is a continuous phase transition at zero temperatue. Due to the strong zero point quantum fluctuations associated with Heisenberg’s uncertainty principle, quantum critical systems are strongly correlated and thus feature many novel emergent phenomena. The superfluid-to-Mott insulator quantum critical point (SF-MI QCP), which can be realized with ultracold atoms in an optical lattice, is one of the simplest examples of quantum criticality. Near the QCP, the system is described by the relativistic ?4 theory with complex field, and thus has emergent Lorentz invariance. The “universe” near the SF-MI QCP mimics the standard model in particle physics, with bosonic atoms corresponding to the relativistic superfluid vacuum, the speed of sound to the speed of light, phonons to massless Goldstone modes and the amplitude mode to Higgs bosons. The emergent amplitude mode (also called massive Goldstone or Higgs mode) has strong decay into phonons in (2+1)-dimensions. Its visiblity in the relevant spectral functions has been controversial for decades. We caculate the spectral function for the kinetic energy using path-integral Monte Carlo simulations and numerical analytical continuation methods, and we find the amplitude mode survives as a well-defined universal finite-width resonance. The frequency dependent universal conductivity at SF-MI QCP received a lot of interest recently as a way of testing the AdS/CFT correspondence from string theory. We find that the AdS/CFT correspondence for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the temperature of the conformal field theory. The requirements for measuring the universal conductivity in an ultacold atoms experiment are also determined by our calculation.

Scratched XY universality class

In 1987, Giamarchi and Schulz showed that in one-dimensional disordered and interacting boson systems there is a quantum phase transition from a superfluid to an insulating state in the weak-disorder limit. This phase transition is driven by the proliferation of vortex–anti-vortex pairs in the mapped 2D classical field. It belongs to the well-known Berezinskii-Kosterlitz-Thouless universality class that is ubiquitous in 1D quantum and 2D classical systems. However, the nature of the phase transition in the strong-disorder regime had been beyond the reach of physicists for nearly 30 years! Inspired by the special role played by potential barriers (weak links) in destroying superfluidity in 1D quantum systems, we developed an asymptotically exact renormalization group theory of superfluid-insulator transitions describing phase transitions in both the strong- and weak-disorder regimes, as well as the crossover between the two. We found that in the strong-disorder regime, weak links can cut the superfluid into disconnected pieces and thus destroy superfluidity, while the proliferation of vortex–anti-vortex pairs remains irrelevant. The new universality class is coined the “scratched XY universality class” since upon (1+1)D mapping, the 1D quantum system is mapped to a 2D classical system with correlated disorder in the form of parallel “scratches”. Based on our theory, for the first time we are able to establish the ground-state phase diagram of the 1D disordered Bose-Hubbard model.