A finite-temperature phase transition for disordered weakly interacting bosons in one dimension

By I. Aleiner, Boris L. Altshuler, G. Shlyapnikov. 2009

136 citations recorded by the source corpus.

It is commonly accepted that there are no phase transitions in one-dimensional systems at a finite temperature, because long-range correlations are destroyed by thermal fluctuations. Here we show theoretically that the one-dimensional gas of short-range interacting bosons in the presence of disorder can undergo a finite-temperature phase transition between two distinct states: fluid and insulator. Neither of these states has long-range spatial correlations, but this is a true, albeit non-conventional, phase transition, because transport properties are singular at the transition point. In the fluid phase, mass transport is possible, whereas in the insulator phase it is completely blocked even at finite temperatures. This study thus provides insight into how the interaction between disordered bosons influences their Anderson localization. This question, first raised for electrons in solids, is now crucial for the studies of atomic bosons, where recent experiments have demonstrated Anderson localization in expanding dilute quasi-one-dimensional clouds.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/dbc87f54306d106ee1ab8e763c2c1c1a5c8821f4

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In Atomic and Molecular Physics, and Optics

1. D. Abanin
2. I. Bloch
3. Maksym Serbyn
4. E. Altman
5. Marcos Rigol
6. V. Ros
7. Antonello Scardicchio
8. E. Demler

Citations in the corpus

• Local integrals of motion in many‐body localized systems (2016, unknown): “This expectation has been made concrete in [28–30], where it was suggested that MBL Hamiltonians are non-linear functionals of a complete set of LIOMs Iα , of the form Hdiag = h0 + ∑ α hα Iα + ∑ α,β hαβ Iα Iβ + ∑ α,β,γ hαβγ Iα Iβ Iγ + · · · , (11) where the dots stand for higher order products.”
• One dimensional bosons: From condensed matter systems to ultracold gases (2011, background): “For small disorder the boundary between the superfluid and the localized phase has recently been reinvestigated (Aleiner et al., 2010; Falco et al., 2009; Lugan et al., 2007), confirming the general shape of Fig.”
• Integrals of motion in the many-body localized phase (2014, background): “Many-body localization opens the interesting possibilities of protection of topological order at finite temperature or of phase transitions below the equilibrium lower critical dimension [18, 19, 20, 21, 22, 23]).”
• Colloquium : Many-body localization, thermalization, and entanglement (2018, background): “This question was investigated for disordered weakly interacting bosons in one and two dimensions by Aleiner et al. (2010) and Bertoli et al. (2017), who argued that the BG phase is smoothly connected to an MBL phase as the temperature is increased.”
• Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality (2013, background): “suggested to exist in the 1 D bosonic case [9], at infinite temperatures as a function of disorder strength [10–12], and”
• One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm (2011, background): “This possibility was raised by Anderson (1958), analyzed in the contexts of disordered solid-state conductors (Basko et al., 2006) and atomic cold gases (Aleiner et al., 2010) recently, and currently receives a considerable attention, see Pal and Huse (2010) and references therein.”