Quantum glass and superglass phases in the random-hopping Bose-Hubbard model

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Abstract: 
A prominent example of glassy physics are spin glasses, where glassiness was induced by off-diagonal disorder. It is intriguing to search for similar behavior in interacting particle systems. A key discovery in this context is the superglass phase, first experimentally observed in solid 4He [1] and initially identified as a supersolid [2]. The uniqueness of this phase comes from the fact that it not only comprises glassiness, but also requires it to compete with superfluidity, as those two orders coexist. Physical systems where this competition can be observed and studied in a controllable way are scarce. However, the development of quantum simulation techniques, e.g., using ultracold atoms in optical lattices, paves the way toward experimental studies of such systems. Combining a theoretical study of a model Hamiltonian with such a simulation will allow for determining the roles of system components and a better understanding of the superglass state. 

I will present a theoretical investigation of such an interacting bosonic system, where in addition to a new glass phase [3], we indeed find and then characterize the superglass phase [4]. 

We describe the system using the Bose-Hubbard Hamiltonian with a random hopping term, in contrast to the broadly explored diagonal disorder case.  To find the state of the system, we use a framework adopted from quantum spin glasses based on applying the replica trick and Trotter-Suzuki expansion to arrive at a set of self-consistent equations, which we then solve numerically. Additionaly, we use the stability of the replica-symmetric solution to find one of the phase transitions [5]. Based on these solutions, we obtain the phase diagrams and characterize the phases. 

On the phase diagram, we identify multiple phases, including new glass and superglass phases, as well as the superfluid and disordered ones. We show the existence of quantum phase transitions [3] and reentrant phase transitions [6] in the system. Additionally, we characterize the phases and find that in the superglass phase the glass order and superfluid order compete with each other [4]. We propose a feasible experimental realization of the system, which enables its future simulation and observation of predicted phases [3]. 

[1] B. Hunt et al., Science 324, 632–636 (2009). 
[2] E. Kim, M. H. W. Chan, Nature 427, 225–227 (2004). 
[3] AP, T. K. Kopeć, Phys. Rev. Lett. 120, 160401 (2018). 
[4] AP, T. K. Kopeć, Phys. Rev. B 105, 174203 (2022). 
[5] AP, T. K. Kopeć, J. Stat. Mech. 2022, 73302 (2022). 
[6] AP, T. K. Kopeć, Phys. A 609, 128360 (2023).