TY - JOUR
T1 - Effective action approach for quantum phase transitions in bosonic lattices
AU - Bradlyn, Barry
AU - Dos Santos, Francisco Ednilson A.
AU - Pelster, Axel
PY - 2009/1/5
Y1 - 2009/1/5
N2 - Based on standard field-theoretic considerations, we develop an effective action approach for investigating quantum phase transitions in lattice Bose systems at arbitrary temperature. We begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, we then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced in the standard way and the underlying effective action is derived via a Legendre transformation. Determining the Ginzburg-Landau expansion to first order in the tunneling term, expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three-dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator-superfluid phase boundary to first order in the tunneling, the predictions of our effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase.
AB - Based on standard field-theoretic considerations, we develop an effective action approach for investigating quantum phase transitions in lattice Bose systems at arbitrary temperature. We begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, we then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced in the standard way and the underlying effective action is derived via a Legendre transformation. Determining the Ginzburg-Landau expansion to first order in the tunneling term, expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three-dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator-superfluid phase boundary to first order in the tunneling, the predictions of our effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase.
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U2 - 10.1103/PhysRevA.79.013615
DO - 10.1103/PhysRevA.79.013615
M3 - Article
AN - SCOPUS:59249103337
SN - 1050-2947
VL - 79
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 1
M1 - 013615
ER -