Spectroscopic shifts as a signature of many-body localization phase transition in a one-dimensional transmon array

Tuure Orell, Alexios A. Michailidis, Maksym Serbyn +1 more

Matti Silveri, Richard Brierley, Xiongjie Yu +1 more

Mohammad Pouranvari, Shiuan-Fan Liou

We introduce characterizations for many-body phase transitions between delocalized and localized phases based on the system's sensitivity to boundary conditions. In particular, we change boundary conditions from periodic to antiperiodic and calculate a shift in the system's energy and shifts in the single-particle density-matrix eigenvalues in the corresponding energy window. We employ the typical model for studying MBL, a one-dimensional disordered system of fermions with nearest-neighbor repulsive interaction where disorder is introduced as randomness on on-site energies. By calculating numerically the shifts in the system's energy and eigenvalues of the single-particle density matrix, we observe that in the localized regime, both shifts are vanishing; while in the extended regime, both shifts are on the order of the corresponding level spacing. We also applied these characterizations of the phase transition to the case of having next-nearest-neighbor interactions in addition to the nearest-neighbor interactions and studied its effect on the transition.

Julian Léonard, Alexander Lukin, Matthew Rispoli +6 more

Miroslav Hopjan, Fabian Heidrich‐Meisner

We numerically investigate one-dimensional Bose-Hubbard chains with on-site disorder by means of exact diagonalization. A primary focus of our work is on characterizing Fock-space localization in this model from the single-particle perspective. For this purpose, we compute the one-particle density matrix (OPDM) in many-body eigenstates. We show that the natural orbitals (the eigenstates of the OPDM) are extended in the ergodic phase and real-space localized when one enters the many-body localization (MBL) phase. Furthermore, the distributions of occupations of the natural orbitals can be used as measures of Fock-space localization in the respective basis. Consistent with previous studies, we observe signatures of a transition from the ergodic to the MBL regime when increasing the disorder strength. We further demonstrate that Fock-space localization, albeit weaker, is also evidently present in the distribution of the physical densities in the MBL regime, for both soft- and hard-core bosons. Moreover, the full distribution of the densities of the physical particles provides a one-particle measure for the detection of the ergodic-MBL transition which could be directly accessed in experiments with ultracold gases.

Zala Lenarčič, Ori Alberton, Achim Rosch +1 more

Coupling a many-body localized system to a thermal bath breaks local conservation laws and washes out signatures of localization. When the bath is nonthermal or when the system is also weakly driven, local conserved quantities acquire a highly nonthermal stationary value. We demonstrate how this property can be used to study the many-body localization phase transition in weakly open systems. Here, the strength of the coupling to the nonthermal baths plays a similar role as a finite temperature in a T=0 quantum phase transition. By tuning this parameter, we can detect key features of the many-body localization (MBL) transition: the divergence of the dynamical exponent due to Griffiths effects in one dimension and the critical disorder strength. We apply these ideas to study the MBL critical point numerically. The possibility to observe critical signatures of the MBL transition in an open system allows for new numerical approaches that overcome the limitations of exact diagonalization studies. Here, we propose a scalable numerical scheme to study the MBL critical point using matrix-product operator solution to the Lindblad equation.