The Gutzwiller projection produces a well-known ansatz for spin-liquid and quantum Hall ground-state wavefunctions that is amenable to numerical simulation, with the Laughlin wavefunction being the most celebrated example. A long-standing issue is the precise relation between the Gutzwiller projection and the closely related parton gauge theory. Here, we clarify this issue by providing a field-theoretic description of the Gutzwiller projection. In a path integral description, the universal physics of the projected state is described in terms of a gauge field supported on a temporal slab of vanishing width
ε→0 coupled to the bulk matter fields. We analytically derive the universal physics of various Gutzwiller projected states. Our construction is also applicable to discrete symmetries, and we use it to analyze various projected SPT states. Among our results, we show that the Gutzwiller projection is not a good ansatz for the long-distance properties of
U(1) Dirac spin liquids, spinon Fermi surface spin liquids or composite Fermi liquids, and that the Gutzwiller projection of a quantum spin Hall state has only quasi-long range order. In contrast, in examples where the gauge field is gapped, including Laughlin states,
Z2 spin liquids and Luttinger liquids, we show that the slab gauge theory from Gutzwiller projection reproduces the correct universal physics of the full parton gauge theory. We also present a generalization of our field theory that describes
G-intertwining defects, with application to self-duality defects of recent theoretical interest.
Ultracold atoms in optical lattices are versatile testbeds to study and manipulate equilibrium and out-of-equilibrium aspects of quantum many-body systems whose behavior can be described by Hubbard-type Hamiltonians. In this paper, we consider an ansatz wave-function which respects total particle-number conservation for such systems and goes beyond mean-field theory; this wave-function has the same complexity in the number of parameters as the mean-field Gutzwiller ansatz, and captures quantum correlations and entanglement via projection onto an effective low-energy manifold. This ansatz can be exploited to study quantum phases observed in a large class of systems realizable in such experimental platforms and is useful to study quantum dynamics. We show that the relaxation dynamics of various out-of-equilibrium initial states under sudden quench of Hamiltonian parameters can be studied with this ansatz wavefunction within the framework of time-dependent variational principle. We present a quantitative comparison with small-scale exact diagonalization results in the 1D Bose-Hubbard model with and without external trapping potentials.
The exciton Bose liquid (EBL) is a hypothesized phase of bosons in
2+1D which possesses a dispersion that is gapless along the coordinate axes in momentum space. The low energy theory of the EBL involves modes on all length scales, extending all the way down to the lattice spacing. In this paper, we discuss a renormalization group scheme that can be used to address the stability of this and related phases of matter. We find that, in the absence of an extensively large symmetry group, realizing the simplest formulation of the EBL always requires fine-tuning. However, we also argue that the addition of certain marginal interactions can be used to realize a stable phase, without the need for fine-tuning. A simple generalization to
3+1D is also discussed.
The exciton Bose liquid (EBL) is a hypothesized phase of bosons in 2+1D which possesses a dispersion that is gapless along the coordinate axes in momentum space. The low energy theory of the EBL involves modes on all length scales, extending all the way down to the lattice spacing. In this note, we discuss an RG scheme that can be used to address the stability of this and related phases of matter. We argue that in the absence of an extensively large symmetry group, realizing the simplest formulation of the EBL always requires fine-tuning. However, we also argue that the addition of certain marginal interactions can likely be used to realize a stable phase, without the need for fine-tuning. A simple generalization to 3+1D is also discussed.
Taking inspiration from the state-of-the art knowledge of the Bose-Hubbard (BH) model and recent methodological developments in its fermionic counterpart, this work deals with the study of the collective dynamics of a lattice Bose gas beyond the mean-field picture through a quantum description of its elementary excitations. The Hamiltonian quantization, performed via a Bogoliubov quadratization of the BH action within the Gutzwiller approach, allows to expand the effective action of the theory up to second order in the fluctuations around the mean-field solution, as well as to prefigure the possibility of identifying the main decay vertices of the collective modes and other effects that are not evident at the second-order level. This quantum description extends the standard Bogoliubov approach to the study of superfluid Bose systems for comprising higher excitation branches, including the Higgs mode in the superfluid phase, and identifies their physical meaning together with appropriate observables which could be taken into consideration for their experimental characterization. The ultimate aim of the quantization procedure is the determination of fundamental quantities as the depletion of the condensate and the effective superfluid fraction, which are not accessible by a mean-field description or not completely characterized in the regime of strong interactions.
A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models. By treating clusters within the Gutzwiller theory, a surprisingly good description of quantum fluctuations beyond the mean-field theory is achieved approaching quantum Monte Carlo predictions for large clusters. Applying this powerful method to the Bose-Hubbard model, we demonstrate that it yields precise results for the superfluid to Mott-insulator transition in square, honeycomb, and cubic lattices. Due to the exact treatment within a cluster, the method can be effortlessly adapted to more complicated Hamiltonians in the fast progressing field of optical lattice experiments. This includes state- and site-dependent superlattices, large confined atomic systems, and disordered potentials, as well as various types of extended Hubbard models. Furthermore, the approach allows an excellent treatment of systems with arbitrary filling factors. We discuss the perspectives that allow for the computation of large, spatially varying lattices, low-lying excitations, and time evolution.