Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492â1505 (1958).
Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: Many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).
Giamarchi, T. & Schulz, H. Anderson localization and interactions in one-dimensional metals. Phys. Rev. B 37, 325â340 (1988).
Fisher, M. P., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluidâinsulator transition. Phys. Rev. B 40, 546â570 (1989).
Viebahn, K., Sbroscia, M., Carter, E., Yu, J.-C. & Schneider, U. Matter-wave diffraction from a quasicrystalline optical lattice. Phys. Rev. Lett. 122, 110404 (2019).
Gautier, R., Yao, H. & Sanchez-Palencia, L. Strongly interacting bosons in a two-dimensional quasicrystal lattice. Phys. Rev. Lett. 126, 110401 (2021).
Choi, J.-Y. et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547â1552 (2016).
Bordia, P. et al. Probing slow relaxation and many-body localization in two-dimensional quasiperiodic systems. Phys. Rev. X 7, 041047 (2017).
Michal, V. P., Aleiner, I. L., Altshuler, B. L. & Shlyapnikov, G. V. Finite-temperature fluidâinsulator transition of strongly interacting 1D disordered bosons. Proc. Natl Acad. Sci. USA 113, E4455âE4459 (2016).
Bertoli, G., Michal, V., Altshuler, B. & Shlyapnikov, G. Finite-temperature disordered bosons in two dimensions. Phys. Rev. Lett. 121, 030403 (2018).
Zhu, Z., Yao, H. & Sanchez-Palencia, L. Thermodynamic phase diagram of two-dimensional bosons in a quasicrystal potential. Phys. Rev. Lett. 130, 220402 (2023).
Ciardi, M., Macrì, T. & Cinti, F. Finite-temperature phases of trapped bosons in a two-dimensional quasiperiodic potential. Phys. Rev. A 105, L011301 (2022).
Scalettar, R. T., Batrouni, G. G. & Zimanyi, G. T. Localization in interacting, disordered, Bose systems. Phys. Rev. Lett. 66, 3144â3147 (1991).
Lugan, P. et al. Ultracold Bose gases in 1D disorder: from Lifshits glass to BoseâEinstein condensate. Phys. Rev. Lett. 98, 170403 (2007).
Altshuler, B., Krovi, H. & Roland, J. Anderson localization makes adiabatic quantum optimization fail. Proc. Natl Acad. Sci. USA 107, 12446â12450 (2010).
Oganesyan, V. & Huse, D. A. Localization of interacting fermions at high temperature. Phys. Rev. B 75, 155111 (2007).
Pal, A. & Huse, D. A. Many-body localization phase transition. Phys. Rev. B 82, 174411 (2010).
Khemani, V., Nandkishore, R. & Sondhi, S. L. Nonlocal adiabatic response of a localized system to local manipulations. Nat. Phys. 11, 560â565 (2015).
Crowell, P. A., Van Keuls, F. W. & Reppy, J. D. Onset of superfluidity in 4He films adsorbed on disordered substrates. Phys. Rev. B 55, 12620â12634 (1997).
Sacépé, B. et al. Localization of preformed Cooper pairs in disordered superconductors. Nat. Phys. 7, 239â244 (2011).
Yu, R. et al. Bose glass and Mott glass of quasiparticles in a doped quantum magnet. Nature 489, 379â384 (2012).
Rapsch, S., Schollwöck, U. & Zwerger, W. Density matrix renormalization group for disordered bosons in one dimension. Europhys. Lett. 46, 559 (1999).
Roux, G. et al. Quasiperiodic BoseâHubbard model and localization in one-dimensional cold atomic gases. Phys. Rev. A 78, 023628 (2008).
Bissbort, U. & Hofstetter, W. Stochastic mean-field theory for the disordered BoseâHubbard model. Europhys. Lett. 86, 50007 (2009).
Söyler, Å. G., Kiselev, M., Prokofâev, N. V. & Svistunov, B. V. Phase diagram of the commensurate two-dimensional disordered BoseâHubbard model. Phys. Rev. Lett. 107, 185301 (2011).
Niederle, A. & Rieger, H. Bosons in a two-dimensional bichromatic quasiperiodic potential: analysis of the disorder in the BoseâHubbard parameters and phase diagrams. Phys. Rev. A 91, 043632 (2015).
Gerster, M. et al. Superfluid density and quasi-long-range order in the one-dimensional disordered BoseâHubbard model. New J. Phys. 18, 015015 (2016).
Yao, H., Giamarchi, T. & Sanchez-Palencia, L. LiebâLiniger bosons in a shallow quasiperiodic potential: Bose glass phase and fractal Mott lobes. Phys. Rev. Lett. 125, 060401 (2020).
Zhang, C., Safavi-Naini, A. & Capogrosso-Sansone, B. Equilibrium phases of two-dimensional bosons in quasiperiodic lattices. Phys. Rev. A 91, 031604 (2015).
Johnstone, D., Ãhberg, P. & Duncan, C. W. The mean-field Bose glass in quasicrystalline systems. J. Phys. A 54, 395001 (2021).
Gadway, B., Pertot, D., Reeves, J., Vogt, M. & Schneble, D. Glassy behavior in a binary atomic mixture. Phys. Rev. Lett. 107, 145306 (2011).
Fallani, L., Lye, J., Guarrera, V., Fort, C. & Inguscio, M. Ultracold atoms in a disordered crystal of light: towards a Bose glass. Phys. Rev. Lett. 98, 130404 (2007).
Deissler, B. et al. Delocalization of a disordered bosonic system by repulsive interactions. Nat. Phys. 6, 354â358 (2010).
DâErrico, C. et al. Observation of a disordered bosonic insulator from weak to strong interactions. Phys. Rev. Lett. 113, 095301 (2014).
Gori, L. et al. Finite-temperature effects on interacting bosonic one-dimensional systems in disordered lattices. Phys. Rev. A 93, 033650 (2016).
Pasienski, M., McKay, D., White, M. & DeMarco, B. A disordered insulator in an optical lattice. Nat. Phys. 6, 677â680 (2010).
Meldgin, C. et al. Probing the Bose glassâsuperfluid transition using quantum quenches of disorder. Nat. Phys. 12, 646â649 (2016).
Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951 (1984).
Steurer, W. Quasicrystals: What do we know? What do we want to know? What can we know? Acta Crystallogr. A 74, 1â11 (2018).
Abrahams, E., Anderson, P., Licciardello, D. & Ramakrishnan, T. Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673â676 (1979).
Szabó, A. & Schneider, U. Mixed spectra and partially extended states in a two-dimensional quasiperiodic model. Phys. Rev. B 101, 014205 (2020).
Roati, G. et al. Anderson localization of a non-interacting BoseâEinstein condensate. Nature 453, 895â898 (2008).
Gottlob, E. & Schneider, U. Hubbard models for quasicrystalline potentials. Phys. Rev. B 107, 144202 (2023).
Pedri, P. et al. Expansion of a coherent array of BoseâEinstein condensates. Phys. Rev. Lett. 87, 220401 (2001).
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39â44 (2002).
Sbroscia, M. et al. Observing localization in a 2D quasicrystalline optical lattice. Phys. Rev. Lett. 125, 200604 (2020).
Braun, S. et al. Emergence of coherence and the dynamics of quantum phase transitions. Proc. Natl Acad. Sci. USA 112, 3641â3646 (2015).
Wall, M. & Carr, L. Dipoleâdipole interactions in optical lattices do not follow an inverse cube power law. New J. Phys. 15, 123005 (2013).
Trotzky, S. et al. Suppression of the critical temperature for superfluidity near the Mott transition: validating a quantum simulator. Nat. Phys. 6, 998â1004 (2009).
Å trkalj, A., Doggen, E. V. & Castelnovo, C. Coexistence of localization and transport in many-body two-dimensional AubryâAndré models. Phys. Rev. B 106, 184209 (2022).
De Roeck, W. & Huveneers, F. Stability and instability towards delocalization in many-body localization systems. Phys. Rev. B 95, 155129 (2017).
Léonard, J. et al. Probing the onset of quantum avalanches in a many-body localized system. Nat. Phys. 19, 481â485 (2023).
Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004).
dâErrico, C. et al. Feshbach resonances in ultracold 39K. New J. Phys. 9, 223 (2007).
Fletcher, R. J. et al. Two- and three-body contacts in the unitary Bose gas. Science 355, 377â380 (2017).
Etrych, J. et al. Pinpointing Feshbach resonances and testing Efimov universalities in 39K. Phys. Rev. Res. 5, 013174 (2023).
Wessel, S., Alet, F., Troyer, M. & Batrouni, G. G. Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices. Phys. Rev. A 70, 053615 (2004).
