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arXiv:2103.15835

Low energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter

Robert D. Pisarski, Alexei M. Tsvelik

Published Mar 29, 2021• 8 citations
arXivHTMLPDF

Abstract

We discuss bosonic models with a moat spectrum, where in momentum space the minimum of the dispersion relation is on a sphere of nonzero radius. For spinless bosons with $O(N)$ symmetry, we emphasize the essential difference between $N=2$ and $N > 2$. When $N=2$, there are two phase transitions: at zero temperature, a transition to a state with Bose condensation, and at nonzero temperature, a transition to a spatially inhomogeneous state. When $N > 2$, previous analysis suggests that a mass gap is generated dynamically at any temperature. In condensed matter, a moat spectrum is important for spin-orbit-coupled bosons. For cold nuclear or quarkyonic matter, we suggest that the transport properties, such as neutrino emission, are dominated by the phonons related to a moat spectrum; also, that at least in the quarkyonic phase the nucleons may be a non-Fermi liquid.

DOI
10.48550/arxiv.2103.15835

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We discuss bosonic models with a moat spectrum, where in momentum space the minimum of the dispersion relation is on a sphere of nonzero radius. For spinless bosons with O(N)O(N)O(N) symmetry, we emphasize the essential difference between N=2N=2N=2 and N>2N > 2N>2. When N=2N=2N=2, there are two phase transitions: at zero temperature, a transition to a state with Bose condensation, and at nonzero temperature, a transition to a spatially inhomogeneous state. When N>2N > 2N>2, previous analysis suggests that a mass gap is generated dynamically at any temperature. In condensed matter, a moat spectrum is important for spin-orbit-coupled bosons. For cold nuclear or quarkyonic matter, we suggest that the transport properties, such as neutrino emission, are dominated by the phonons related to a moat spectrum; also, that at least in the quarkyonic phase the nucleons may be a non-Fermi liquid.
We study dilute two-dimensional systems of interacting excitons with a moat dispersion, whose ground-state manifold consists of a set of discrete or continuously degenerate energy minima. At low densities and in the presence of contact interactions, it is known that the bosons can undergo statistical transmutation and give rise to a chiral spin liquid. Here, we show that long-range interactions such as those expected in excitonic systems introduce a rich competition between the chiral spin liquid and different kinds of Bose-Einstein condensates. The moat dispersion can favor Bose-Einstein condensation into states occupying multiple momenta, leading to inhomogeneous and supersolid phases with a highly anisotropic superfluid response. We demonstrate that a proper TTT-matrix renormalization of the exciton-exciton interaction is essential for describing these phases and show that they can arise even from purely repulsive interactions. This formalism is employed to obtain the phase diagram of competing homogeneous and stripe condensates with the chiral spin liquid in an electron-hole bilayer model. In addition, we show how the TTT matrix enters the familiar Gross-Pitaevskii framework and map out extended phase diagrams within a pseudopotential approximation. We place our findings in the context of real excitonic systems by discussing the roles of finite lifetimes, disorder, band-structure warping, and nonzero temperatures. We conclude that moat bands can drive Bose-Einstein condensation and supersolidity already at weak coupling, in contrast to the case of a standard parabolic dispersion.
The spectrum of elementary excitations in the system of interacting Bose- and Fermi-particles was obtained at a temperature of absolute zero (Dose- condensation being taken into account by means of the Bogolyabov canonic transformations. In terms of a model of permeable spheres'' with finite repulsion it(is shown that the boson spectrum omega (p) in a definite region of parameter has the minimum at p = 0. By selecting parameters one succeeds in obtaining a quite satisfactory quantitative agreement of the theoretical and experimental spectra for superfluid helium. In the case when the Fermi energy is considerably higher than the bosorins maximum energy, a gap characterizing bond energy of the copper pairs can appear in the fermion speetrum due to exchange of virtual supercondensate'' bosons. If in this case the interaction between fermions at infinity is of attraction character, then under certain conditions sustained longitudinal collective excitations of Pose-type with a finite gap'' in the energy spectrum may exist in the superfluid fermion subsystem. Possibility of appearance of similar excitations in superfluid nuclear matter of neutron stars (pulsars) due to gravitational interaction between nucleons is discussed. (auth)
We experimentally engineer a moatlike dispersion in a system of weakly interacting bosons. By periodically modulating the amplitude of a checkerboard optical lattice, the two lowest isolated bands are hybridized such that the single particle energy displays a continuum of nearly degenerate minima that lie along a circle in reciprocal space. The moatlike structure is confirmed by observing a zero group velocity at nonzero quasimomentum and we directly observe the effect of the modified dispersion on the trajectory of the center of mass position of the condensate. We measure the lifetime of condensates loaded into different moat bands at different quasimomenta and compare to theoretical predictions based on a linear stability analysis of Bogoliubov excitations. We find that the condensate decay increases rapidly as the quasimomentum is decreased below the radius of the moat minimum, and argue that such dynamical instability is characteristic of moatlike dispersions, including spin-orbit coupled systems. The ground state of strongly interacting bosons in such degenerate energy landscapes is expected to be highly correlated, and our work represents a step toward realizing fractional quantum Hall-like states of bosons in an optical lattice.
The ground-state energy of infinite symmetric nuclear matter is usually described by strongly interacting nucleons obeying the Pauli exclusion principle. We can imagine a unitary transformation which groups four nonidentical nucleons (i.e., with different spin and isospin) close in coordinate space. Those nucleons, being nonidentical, do not obey the Pauli principle, thus their relative momenta are negligibly small (just to fulfill the Heisenberg principle). Such a cluster can be identified with an $\ensuremath{\alpha}$ boson. But in dense nuclear matter, those $\ensuremath{\alpha}$ particles still obey the Pauli principle since are constituted of fermions. The ground state energy of nuclear matter $\ensuremath{\alpha}$ clusters is the same as for nucleons, thus it is degenerate. We could think of $\ensuremath{\alpha}$ particles as vortices which can now braid, for instance making 8Be^{8}\mathrm{Be}8Be which leave the ground state energy unchanged. Further braiding to heavier clusters (12C^{12}\mathrm{C}12C, 16O^{16}\mathrm{O}16O,…,\dots{},…) could give a different representation of the ground state at no energy cost. In contrast ddd-like clusters (i.e., N=ZN=ZN=Z odd-odd nuclei, where NNN and ZZZ are the neutron and proton number, respectively) cannot describe the ground state of nuclear matter and can be formed at high excitation energies (or temperatures) only. We show that even-even, N=ZN=ZN=Z, clusters could be classified as non-Abelian states of matter. As a consequence an $\ensuremath{\alpha}$ condensate in nuclear matter might be hindered by the Fermi motion, while it could be possible a condensate of 8Be^{8}\mathrm{Be}8Be or heavier clusters.
We formulate and investigate a quantum state, the chiral vortex-line liquid (CVLL), emerging in three-dimensional interacting Bose systems exhibiting moat-band dispersions. Such dispersions feature extensive degeneracy along closed manifolds in momentum space, significantly amplifying quantum fluctuations that suppress conventional Bose-Einstein condensation. By extending the two-dimensional Chern-Simons (CS) flux-attachment transformation to three dimensions through a combination of planar CS phases and Jordan-Wigner fermionization along vortex lines, we construct the CVLL state, characterized by preserved rotational S O ( 2 ) symmetry, broken time-reversal symmetry, nontrivial vortex-line excitations, and topological gapless edge surface states. We construct the associated field theory in a curved spatial geometry and analyze the low-energy effective theory of the CVLL state, demonstrating its topological nature. Using Monte Carlo simulations, we numerically determine the scaling of the chemical potential of the CVLL ground state as a function of boson density for interacting bosons in a cylindrical moat-band geometry and demonstrate that the CVLL phase energetically outcompetes traditional condensate phases at low densities, highlighting its relevance to experimental platforms including frustrated quantum magnets, ultracold atomic gases, excitonic systems, the physics of rotons in He 4 , and moat regimes in heavy-ion collisions.
The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.