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Register a new userDynamical quantum phase transitions in many-body localized systems
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We investigate dynamical quantum phase transitions in disordered quantum many-body models that can support many-body localized phases. Employing $l$-bits formalism, we lay out the conditions for which singularities indicative of the transitions appear in the context of many-body localization. Using the combination of the mapping onto $l$-bits and exact diagonalization results, we explicitly demonstrate the presence of these singularities for a candidate model that features many-body localization. Our work paves the way for understanding dynamical quantum phase transitions in the context of many-body localization, and elucidating whether different phases of the latter can be detected from analyzing the former. The results presented are experimentally accessible with state-of-the-art ultracold-atom and ion-trap setups.
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Precise nature of MBL transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here we investigate MBL transitions in one-dimensional ($d!=!1$) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent $ u!approx!2.4$, which respects the Harris-Luck bound ($ u!>!1/d$) for QP systems. Note that $ u!approx! 2.4$ for QP systems also satisfies the Harris-CCFS bound ($ u!>!2/d$) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure $ u$ of QP-induced MBL transitions.
The resilience of quantum entanglement to a classicality-inducing environment is tied to fundamental aspects of quantum many-body systems. The dynamics of entanglement has recently been studied in the context of measurement-induced entanglement transitions, where the steady-state entanglement collapses from a volume-law to an area-law at a critical measurement probability $p_{c}$. Interestingly, there is a distinction in the value of $p_{c}$ depending on how well the underlying unitary dynamics scramble quantum information. For strongly chaotic systems, $p_{c} > 0$, whereas for weakly chaotic systems, such as integrable models, $p_{c} = 0$. In this work, we investigate these measurement-induced entanglement transitions in a system where the underlying unitary dynamics are many-body localized (MBL). We demonstrate that the emergent integrability in an MBL system implies a qualitative difference in the nature of the measurement-induced transition depending on the measurement basis, with $p_{c} > 0$ when the measurement basis is scrambled and $p_{c} = 0$ when it is not. This feature is not found in Haar-random circuit models, where all local operators are scrambled in time. When the transition occurs at $p_{c} > 0$, we use finite-size scaling to obtain the critical exponent $ u = 1.3(2)$, close to the value for 2+0D percolation. We also find a dynamical critical exponent of $z = 0.98(4)$ and logarithmic scaling of the R{e}nyi entropies at criticality, suggesting an underlying conformal symmetry at the critical point. This work further demonstrates how the nature of the measurement-induced entanglement transition depends on the scrambling nature of the underlying unitary dynamics. This leads to further questions on the control and simulation of entangled quantum states by measurements in open quantum systems.
The existence of many-body mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the many-body localization phenomenon. Here we propose that this issue can be settled in experiments by investigating the time evolution of local degrees of freedom, tailored for specific energies and initial states. An interacting model of spinless fermions with exponentially long-ranged tunneling amplitudes, whose non-interacting version known to display single-particle mobility edges, is used as the starting point upon which nearest-neighbor interactions are included. We verify the manifestation of many-body mobility edges by using numerous probes, suggesting that one cannot explain their appearance as merely being a result of finite-size effects.
We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough $textit{qualitative}$ level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus we show that this MBL transition is in a new universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $ u rightarrow infty$, but the divergence is weaker than for the KT transition.
We investigate a spatial subsystem entropy extracted from the one-particle density matrix (OPDM) in one-dimensional disordered interacting fermions that host a many-body localized (MBL) phase. Deep in the putative MBL regime, this OPDM entropy exhibits the salient features of localization, despite not being a proper entanglement measure. We numerically show that the OPDM entropy of the eigenstates obeys an area law. Similar to the von-Neumann entropy, the OPDM entropy grows logarithmically with time after a quantum quench, albeit with a different prefactor. Both these features survive at moderately large interactions and well towards the transition into the ergodic phase. The computational cost to calculate the OPDM entropy scales only polynomially with the system size, suggesting that the OPDM provides a promising starting point for developing diagnostic tools for MBL in simulations and experiments.
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