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arXiv:2605.30746

Superconductor-"Metal" Transition of One-dimensional Interacting Bosons with Ohmic Quantum Dissipation

Miguel A. Cazalilla

cond-mat.mes-hallcond-mat.quant-gascond-mat.str-elcond-mat.supr-conquant-phSubmitted May 29, 2026• Announced Jun 1, 2026• 0 citations
v1 · May 29, 2026v2 · Jun 16, 2026
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Abstract

The phase diagram of a system of interacting bosons (Cooper pairs) hoping on a one-dimensional (1D) lattice with onsite phase dissipation describing the Josephson tunneling to a nearby diffusive normal-metal electrode is studied. Starting from the system at commensurate lattice filling, it is shown by a combination of analytical techniques that the phase diagram contains two quantum phases: A dissipative Bose-Einstein condensate (D-BEC) or superconductor with long-range phase coherence, and a dissipative Mott insulator (D-Mott) or "metal" with exponentially decaying phase correlations in space and local imaginary-time correlations decaying as the local pairing correlations of the electrode. The D-Mott/metal phase can be described as a 1D array of dissipative boson puddles, weakly coupled by Josephson tunneling. The puddle size roughly corresponds to the length scale beyond which phase slips suppress phase coherence. The dissipative time-dependent Ginsburg-Landau theory phenomenologically used by Sachdev, Werner, and Troyer [Phys. Rev. Lett. {\bf 92} 237003 (2004)] for the superconductor-metal transition in quasi-1D wires is derived from this microscopic puddle picture. Thus, the criticality of the D-Mott/D-BEC transition is shown to belong to the Wilson-Fisher universality class with dynamical exponent $z\approx 2$. At small doping, the D-Mott/metal phase remains stable due to its finite compressibility, which is computed to leading order in a perturbation expansion of the dissipation strength and the inter-puddle Josephson coupling. At larger doping, using a mapping to a pseudospin chain combined with bosonization, the D-BEC/superconductor phase is the ground state for non-vanishing but arbitrarily small dissipation. Similarities and differences with deconfinement transition of an array 1D bosonic Mott insulators in anisotropic optical lattices are also discussed.

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23 pages + 3 figures

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The phase diagram of a system of interacting bosons (Cooper pairs) hoping on a one-dimensional (1D) lattice with onsite phase dissipation describing the Josephson tunneling to a nearby diffusive normal-metal electrode is studied. Starting from the system at commensurate lattice filling, it is shown by a combination of analytical techniques that the phase diagram contains two quantum phases: A dissipative Bose-Einstein condensate (D-BEC) or superconductor with long-range phase coherence, and a dissipative Mott insulator (D-Mott) or "metal" with exponentially decaying phase correlations in space and local imaginary-time correlations decaying as the local pairing correlations of the electrode. The D-Mott/metal phase can be described as a 1D array of dissipative boson puddles, weakly coupled by Josephson tunneling. The puddle size roughly corresponds to the length scale beyond which phase slips suppress phase coherence. The dissipative time-dependent Ginsburg-Landau theory phenomenologically used by Sachdev, Werner, and Troyer [Phys. Rev. Lett. {\bf 92} 237003 (2004)] for the superconductor-metal transition in quasi-1D wires is derived from this microscopic puddle picture. Thus, the criticality of the D-Mott/D-BEC transition is shown to belong to the Wilson-Fisher universality class with dynamical exponent z≈2z\approx 2z≈2. At small doping, the D-Mott/metal phase remains stable due to its finite compressibility, which is computed to leading order in a perturbation expansion of the dissipation strength and the inter-puddle Josephson coupling. At larger doping, using a mapping to a pseudospin chain combined with bosonization, the D-BEC/superconductor phase is the ground state for non-vanishing but arbitrarily small dissipation. Similarities and differences with deconfinement transition of an array 1D bosonic Mott insulators in anisotropic optical lattices are also discussed.
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We review the nature of superfluid ground states and the universality of their properties with emphasis to Bose Einstein Condensate systems in atomic physics. We then study the superfluid Mott transition in such systems. We find that there could be two types of Mott transitions and phases. One of them was described long ago and corresponds to suppression of Josephson tunneling within superfluids sitting at each well. On the other hand, the conditions of optical lattice BEC experiments are such that either the coherence length is longer than the interwell separation, or there is too small a number of bosons per well. This vitiates the existence of a superfluid order parameter within a well, and therefore of Josephson tunneling between wells. Under such conditions, there is a transition to a Mott phase which corresponds to suppression of individual boson tunneling among wells. This last transition is in general discontinuous and can happen for incommensurate values of bosons per site. If the coherence length is small enough and the number of bosons per site large enough, the transition studied in the earlier work will happen.
The ground states of bosons have been classified into superfluids, bosonic quantum Hall states, Mott insulators, and Bose glass. Recent experiments in two-dimensional clean superconductors under an external magnetic field BBB strongly suggest the existence of the fourth quantum state of Cooper pairs, i.e., Bose metal or quantum metal, where the resistivity remains constant at lowest temperature. However, its theoretical understanding remains unsettled. In this paper, we propose a model where the vortices behave as quantum bosons subject to dissipation at the normal core. We discuss that those bosons remain metallic even at zero temperature by generalizing the Feynman picture of superfluidity in the first quantization formulation and also by a perturbative calculation for a field theoretical model in the second quantization formalism. This result indicates that the resistivity $\ensuremath{\rho}$ of Bose metal at zero temperature behaves as $\ensuremath{\rho}\ensuremath{\sim}{\ensuremath{\rho}}_{n}(B/{B}_{c2})$ with ${\ensuremath{\rho}}_{n}$ being the residual resistivity in the normal state and Bc2{B}_{c2}Bc2​ the second upper critical field. It also predicts that the Bose metal is missing in superclean superconductors and at the dirty limit or in granular superconductors.
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