Real-Frequency Response Functions at Finite Temperature.

Building on previous developments [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019); PRBMDO2469-995010.1103/PhysRevB.99.035120A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B101, 125109 (2020); PRBMDO2469-995010.1103/PhysRevB.101.125109A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B102, 045115 (2020)PRBMDO2469-995010.1103/PhysRevB.102.045115, B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998)PRBMDO0163-182910.1103/PhysRevB.57.2108, J. Vicicevic and M. Ferrero, Phys. Rev. B 101, 075113 (2020)PRBMDO2469-995010.1103/PhysRevB.101.075113], we show that the diagrammatic Monte Carlo technique allows us to compute finite-temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system's action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows us to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. For illustrative purposes we consider the problem of the plasmon linewidth in a homogeneous electron gas (jellium).

Extended Crossover from a Fermi Liquid to a Quasiantiferromagnet in the Half-Filled 2D Hubbard Model.

The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.

Contact and Momentum Distribution of the Unitary Fermi Gas.

A key quantity in strongly interacting resonant Fermi gases is the contact C, which characterizes numerous properties such as the momentum distribution at large momenta or the pair correlation function at short distances. The temperature dependence of C was measured at unitarity, where existing theoretical predictions differ substantially even at the qualitative level. We report accurate data for the contact and the momentum distribution of the unitary gas in the normal phase, obtained by bold diagrammatic Monte Carlo and Borel resummation. Our results agree with experimental data within error bars and provide crucial benchmarks for the development of advanced theoretical treatments and precision measurements.

Deconfined criticality flow in the Heisenberg model with ring-exchange interactions.

Quantum transition points in the J-Q model--the test bed of the deconfined critical point theory--and the SU(2)-symmetric discrete noncompact CP(1) representation of the deconfined critical action are directly compared by the flowgram method. We find that the flows of two systems coincide in a broad region of linear system sizes (10 < L < 50 for the J-Q model), implying that the deconfined critical point theory correctly captures the mesoscopic physics of competition between the antiferromagnetic and valence-bond orders in quantum spin systems. At larger sizes, however, we observe significant deviations between the two flows which both demonstrate strong violations of scale invariance. This reliably rules out the second-order transition scenario in at least one of the two models and suggests the most likely explanation for the nature of the transition in the J-Q model.

Bold diagrammatic Monte Carlo method applied to fermionized frustrated spins.

We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing--cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate the magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures. The extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine the implications of this unusual scenario.

Role of Bose statistics in crystallization and quantum jamming.

The indistinguishability of particles is a crucial factor destabilizing crystalline order in Bose systems. We describe this effect in terms of damped quasiparticle modes and in the dual language of Feynman paths, and illustrate it by first-principles simulations of dipolar bosons and bulk condensed 4He. The first major implication is that, contrary to conventional wisdom, zero-point motion alone cannot prevent 4He crystallization at near zero pressure. Second, Bose statistics leads to quantum jamming at finite temperature, dramatically enhancing the metastability of superfluid glasses. Only studies of indistinguishable particles can reliably address these issues.

Higgs mode in a two-dimensional superfluid.

We present solid evidence for the existence of a well-defined Higgs amplitude mode in two-dimensional relativistic field theories based on analytically continued results from quantum Monte Carlo simulations of the Bose-Hubbard model in the vicinity of the superfluid-Mott insulator quantum critical point, featuring emergent particle-hole symmetry and Lorentz invariance. The Higgs boson, seen as a well-defined low-frequency resonance in the spectral density, is quickly pushed to high energies in the superfluid phase and disappears by merging with the broad secondary peak at the characteristic interaction scale. Simulations of a trapped system of ultracold (87)Rb atoms demonstrate that the low-frequency resonance is lost for typical experimental parameters, while the characteristic frequency for the onset of a strong response is preserved.

Phase diagram of the commensurate two-dimensional disordered Bose-Hubbard model.

We establish the full ground state phase diagram of the disordered Bose-Hubbard model in two dimensions at a unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid-insulator transition of the pure system, we observe an unexpectedly weak--almost not resolvable--sensitivity of the critical interaction to the strength of (weak) disorder.

Criticality in trapped atomic systems.

We discuss generic limits posed by the trap in atomic systems on the accurate determination of critical parameters for second-order phase transitions, from which we deduce optimal protocols to extract them. We show that under current experimental conditions the in situ density profiles are barely suitable for an accurate study of critical points in the strongly correlated regime. Contrary to recent claims, the proper analysis of time-of-fight images yields critical parameters accurately.

Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipole systems.

The superfluid to normal fluid transition of dipolar bosons in two dimensions is studied in a broad density range by using path integral Monte Carlo simulations and summarized in the phase diagram. While at low densities we find good agreement with the universal results depending only on the scattering length a{s}, at moderate and high densities the transition temperature is strongly affected by interactions and the excitation spectrum of quasiparticles. The results are expected to be of relevance to dipolar atomic and molecular systems and indirect excitons in quantum wells.

Sharp transition for single polarons in the one-dimensional Su-Schrieffer-Heeger model.

We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength λ, in all models where this coupling depends only on phonon momentum q. In the SSH model the coupling also depends on the electron momentum k; we find it has a sharp transition, at a critical coupling strength λ(c), between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at λ=λ(c). This result is representative of all polarons with coupling depending on k and q, and will have important experimental consequences (e.g., in angle-resolved photoemission spectroscopy and conductivity experiments).

Absence of a direct superfluid to mott insulator transition in disordered bose systems.

We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove the compressibility of the system on the superfluid-insulator critical line and in its neighborhood. These conclusions follow from a general theorem of inclusions, which states that for any transition in a disordered system, one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: the critical disorder bound Delta(c) corresponding to the onset of disorder-induced superfluidity, satisfies the relation Delta(c)>Eg/2, with Eg/2 the half-width of the Mott gap in the pure system.

Underlying mechanism for the giant isochoric compressibility of solid (4)He: superclimb of dislocations[ corrected].

In the experiment on superfluid transport in solid 4He [Phys. Rev. Lett. 100, 235301 (2008)], Ray and Hallock observed an anomalously large isochoric compressibility: the supersolid samples demonstrated a significant and apparently spatially uniform response of density and pressure to chemical potential, applied locally through Vycor "electrodes." We propose that the effect is due to superclimb: edge dislocations can climb because of mass transport along superfluid cores. We corroborate the scenario by ab initio simulations of an edge dislocation in solid 4He at T = 0.5 K. We argue that at low temperature the effect must be suppressed due to a crossover to the smooth dislocation.

Superfluid transition in a bose gas with correlated disorder.

The superfluid transition of a three-dimensional gas of hard-sphere bosons in a disordered medium is studied using quantum Monte Carlo methods. Simulations are performed in continuous space both in the canonical and in the grand-canonical ensemble. At fixed density we calculate the shift of the transition temperature as a function of the disorder strength, while at fixed temperature we determine both the critical chemical potential and the critical density separating normal and superfluid phases. In the regime of strong disorder the normal phase extends up to large values of the degeneracy parameter, and the critical chemical potential exhibits a linear dependence in the intensity of the random potential. The role of interactions and disorder correlations is also discussed.

Binding of a 3He impurity to a screw dislocation in solid 4He.

Using first-principles simulations for the probability density of finding a 3He atom in the vicinity of the screw dislocation in solid 4He, we determine the binding energy to the dislocation nucleus E(B)=0.8+/-0.1 K and the density of localized states at larger distances. The specific heat due to 3He features a peak similar to the one observed in recent experiments, and our model can also account for the observed increase in shear modulus at low temperature. We further discuss the role of 3He in the picture of superfluid defects.

Expansion of a quantum gas released from an optical lattice.

We analyze the interference pattern produced by ultracold atoms released from an optical lattice, commonly interpreted as the momentum distributions of the trapped quantum gas. We show that for finite times of flight the resulting density distribution can, however, be significantly altered, similar to a near-field diffraction regime in optics. We illustrate our findings with a simple model and realistic quantum Monte Carlo simulations for bosonic atoms and compare the latter to experiments.

Local stress and superfluid properties of solid 4He.

We provide a semiquantitative tool, derived from first-principles simulations, for answering the question of whether certain types of defects in solid 4He support mass superflow. Although ideal crystals of 4He are not supersolid, the gap for vacancy creation closes when applying a moderate stress. While a homogeneous system becomes unstable at this point, the stressed core of crystalline defects (dislocations and grain boundaries) can turn superfluid.

Deconfined criticality: generic first-order transition in the SU(2) symmetry case.

Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first-order transition, similar to the case of U(1) x U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.