Abstract
We study the low-temperature limit of the d-dimensional imperfect Bose gas. Relying on an exact analysis of the microscopic model, we establish the existence of a second-order quantum phase transition to a phase involving the Bose–Einstein condensate. The transition is triggered by varying the chemical potential and persists at non-zero temperatures T for d > 2. We extract the exact phase diagram and identify the scaling regimes in the vicinity of the quantum-critical point focusing on the behavior of the correlation length ξ. The length ξ develops an essential singularity exclusively for d = 2. We follow the evolution of the phase diagram varying d. For d > 2 our results agree with renormalization-group-based analysis of the effective bosonic order-parameter models with the dynamical exponent z = 2.
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