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arXiv:2011.13757 · New Journal of Physics

Impurity dephasing in a Bose–Hubbard model

Fabio Caleffi, Massimo Capone, Inés de Vega, Alessio Recati

Published Jan 27, 2021• 11 citations
arXivHTMLPDF

Abstract

Abstract We study the dynamics of a two-level impurity embedded in a two-dimensional Bose–Hubbard (BH) model at zero temperature from an open quantum system perspective. Results for the decoherence across the whole phase diagram are presented, with a focus on the critical region close to the transition between superfluid and Mott insulator. In particular we show how the decoherence and the deviation from a Markovian behaviour are sensitive to whether the transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the BH environment and its non-Gaussian statistics, beyond the standard independent boson model, is highlighted. Our analysis resorts on a recently developed method (2020 Phys. Rev. Res. 2 033276) – closely related to slave boson approaches – that enables us to capture the correlations across the whole phase diagram. This semi-analytical method provides us with a deep insight into the physics of the spin decoherence in the superfluid and Mott phases as well as close to the phase transitions.

DOI
10.1088/1367-2630/abe080

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Abstract We study the dynamics of a two-level impurity embedded in a two-dimensional Bose–Hubbard (BH) model at zero temperature from an open quantum system perspective. Results for the decoherence across the whole phase diagram are presented, with a focus on the critical region close to the transition between superfluid and Mott insulator. In particular we show how the decoherence and the deviation from a Markovian behaviour are sensitive to whether the transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the BH environment and its non-Gaussian statistics, beyond the standard independent boson model, is highlighted. Our analysis resorts on a recently developed method (2020 Phys. Rev. Res. 2 033276) – closely related to slave boson approaches – that enables us to capture the correlations across the whole phase diagram. This semi-analytical method provides us with a deep insight into the physics of the spin decoherence in the superfluid and Mott phases as well as close to the phase transitions.
We study the entanglement entropy and entanglement spectrum of the paradigmatic Bose-Hubbard model, describing strongly correlated bosons on a lattice. The use of a controlled approximation-the slave-boson approach-allows us to study entanglement in all regimes of the model (and, most importantly, across its superfluid-Mott-insulator transition) at a minimal cost. We find that the area-law scaling of entanglement-verified in all the phases-exhibits a sharp singularity at the transition. The singularity is greatly enhanced when the transition is crossed at fixed, integer filling, due to a richer entanglement spectrum containing an additional gapless mode, which descends from the amplitude (Higgs) mode of the global excitation spectrum-while this mode remains gapped at the generic (commensurate-incommensurate) transition with variable filling. Hence, the entanglement properties contain a unique signature of the two different forms of bosonic criticality exhibited by the Bose-Hubbard model.
A mobile impurity particle immersed in a quantum degenerate gas leads to the formation of a quasiparticle, which can serve as a sensor for its environment. Here, we develop a unified wave function description of an impurity in a two-dimensional Bose-Hubbard model across the Mott-insulator to superfluid transition. Using a multi-mode variational ansatz based on the quantum Gutzwiller approach, we show that the impurity can form several kinds of polaronic and molecular states. In addition to their spectral properties, the wave function provides direct access to the microscopic structure of these states, and we demonstrate that strong correlations in the critical regime of the quantum phase transition give rise to several non-analytic features in the polaron properties. Increasing the impurity-boson interaction leads to transitions between polaron and molecular ground states, and the number of bosons in the impurity dressing cloud grows rapidly at the quantum critical point as the bath modes soften. We furthermore reveal qualitatively distinct non-equilibrium many-body dynamics after the injection of the impurity in the different phases of the Bose-Hubbard model. Our spectral, real space, and dynamical predictions describe complementary properties of polarons in a strongly correlated bosonic bath, which can be observed using current techniques with atoms in optical lattices.
We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram is constructed in terms of the disorder strength and the chemical potential. Via Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where the Mott-insulator-to-superfluid transition occurs, from the strong-disorder regime, where the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.35\ifmmode\pm\else\textpm\fi{}0.05$ and the correlation length critical exponent $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.67\ifmmode\pm\else\textpm\fi{}0.03$. We suggest that the proliferation of the particle-hole pairs screens out the weak-disorder effects.
We present a universal theory for the critical behavior of an impurity at the two-dimensional superfluid--Mott-insulator transition. Our analysis is motivated by a numerical study of the Bose-Hubbard model with an impurity site by Huang et al. [Phys. Rev. B 94, 220502 (2016)]; they found an impurity phase transition as a function of the trapping potential, while the bulk was critical. The bulk theory is described by the O(2)\text{O}(2)O(2) symmetric Wilson-Fisher conformal field theory, and we model the impurity by a localized spin-1/2 degree of freedom. We also consider a generalized model by considering an O(N)\text{O}(N)O(N) symmetric bulk theory coupled to a spin-SSS degree of freedom. We study this field theory using the $\ensuremath{\epsilon}=3\ensuremath{-}d$ expansion, where the impurity-bulk interaction flows to an infrared stable fixed point at the critical trapping potential. We determine the scaling dimensions of the impurity degree of freedom and the associated critical exponents near the critical point. We also determine the universal contribution of the impurity to the finite-temperature compressibility of the system at criticality. Our results are compared with numerical simulations.
We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.
We study the zero-temperature phase transitions of a two-dimensional disordered boson Hubbard model at incommensurate boson densities. Via matrix diagonalization and quantum Monte Carlo simulations, we construct the phase diagram and evaluate the correlation length exponent $\ensuremath{\nu}.$ In the presence of weak disorder, we obtain $\ensuremath{\nu}=0.5\ifmmode\pm\else\textpm\fi{}0.1,$ the same value as that in the pure model, near the tip of a Mott insulator lobe, using the dynamical critical exponent z=2.z=2.z=2. As the strength of disorder is increased beyond a certain value, however, the value of $\ensuremath{\nu}$ is found to change to $0.9\ifmmode\pm\else\textpm\fi{}0.1.$ This result strongly suggests that there exist direct Mott insulator-to-superfluid transitions around the tip of a Mott insulator lobe in the weak disorder regime.