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Register a new userUniversal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
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Non-unitary evolution can give rise to novel steady states classified by their entanglement properties. In this work, we aim to understand its interplay with long-range hopping that decays with $r^{-alpha}$ in free-fermion systems. We first study two solvable Brownian models with long-range non-unitary dynamics: a large-$N$ SYK$_2$ chain and a single-flavor fermion chain and we show that they share the same phase diagram. When $alpha>0.5$, we observe two critical phases with subvolume entanglement scaling: (i) $alpha>1.5$, a logarithmic phase with dynamical exponent $z=1$ and logarithmic subsystem entanglement, and (ii) $0.5<alpha<1.5$, a fractal phase with $z=frac{2alpha-1}{2}$ and subsystem entanglement $S_Apropto L_A^{1-z}$, where $L_A$ is the length of the subsystem $A$. These two phases cannot be distinguished by the purification dynamics, in which the entropy always decays as $L/T$. We then confirm that the results are also valid for the static SYK$_2$ chain, indicating the phase diagram is universal for general free-fermion systems. We also discuss phase diagrams in higher dimensions and the implication in measurement-induced phase transitions.
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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.
Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low (i.e. area law) entanglement, in contrast with the volume law entanglement produced by generic pure unitary time evolution. While the simplest Bell pair model has area law entanglement for any measurement rate, as seen in certain non-interacting systems, we show that more generic models of entanglement can feature an area-to-volume law transition at a critical value of the measurement rate, in agreement with recent numerical investigations. As a concrete example of these ideas, we analytically investigate Clifford evolution in qubit systems which can exhibit an entanglement transition. We are able to identify stabilizer size distributions characterizing the area law, volume law and critical fixed points. We also discuss Floquet random circuits, where the answers depend on the order of limits - one order of limits yields area law entanglement for any non-zero measurement rate, whereas a different order of limits allows for an area law - volume law transition. Finally, we provide a rigorous argument that a system subjected to projective measurements can only exhibit a volume law entanglement entropy if it also features a subleading correction term, which provides a universal signature of projective dynamics in the high-entanglement phase. Note: The results presented here supersede those of all previou
Disorder-free localization has recently emerged as a mechanism for ergodicity breaking in homogeneous lattice gauge theories. In this work we show that this mechanism can lead to unconventional states of quantum matter as the absence of thermalization lifts constraints imposed by equilibrium statistical physics. We study a Kitaev honeycomb model in a skew magnetic field subject to a quantum quench from a fully polarized initial product state and observe nonergodic dynamics as a consequence of disorder-free localization. We find that the system exhibits a subballistic power-law entanglement growth and quantum correlation spreading, which is otherwise typically associated with thermalizing systems. In the asymptotic steady state the Kitaev model develops volume-law entanglement and power-law decaying dimer quantum correlations even at a finite energy density. Our work sheds light onto the potential for disorder-free localized lattice gauge theories to realize quantum states in two dimensions with properties beyond what is possible in an equilibrium context.
We prove the existence of non-equilibrium phases of matter in the prethermal regime of periodically-driven, long-range interacting systems, with power-law exponent $alpha > d$, where $d$ is the dimensionality of the system. In this context, we predict the existence of a disorder-free, prethermal discrete time crystal in one dimension -- a phase strictly forbidden in the absence of long-range interactions. Finally, using a combination of analytic and numerical methods, we highlight key experimentally observable differences between such a prethermal time crystal and its many-body localized counterpart.
Models for non-unitary quantum dynamics, such as quantum circuits that include projective measurements, have been shown to exhibit rich quantum critical behavior. There are many complementary perspectives on this behavior. For example, there is a known correspondence between d-dimensional local non-unitary quantum circuits and tensor networks on a D=(d+1)-dimensional lattice. Here, we show that in the case of systems of non-interacting fermions, there is furthermore a full correspondence between non-unitary circuits in d spatial dimensions and unitary non-interacting fermion problems with static Hermitian Hamiltonians in D=(d+1) spatial dimensions. This provides a powerful new perspective for understanding entanglement phases and critical behavior exhibited by non-interacting circuits. Classifying the symmetries of the corresponding non-interacting Hamiltonian, we show that a large class of random circuits, including the most generic circuits with randomness in space and time, are in correspondence with Hamiltonians with static spatial disorder in the ten Altland-Zirnbauer symmetry classes. We find the criticality that is known to occur in all of these classes to be the origin of the critical entanglement properties of the corresponding random non-unitary circuit. To exemplify this, we numerically study the quantum states at the boundary of Haar-random Gaussian fermionic tensor networks of dimension D=2 and D=3. We show that the most general such tensor network ensemble corresponds to a unitary problem of non-interacting fermions with static disorder in Altland-Zirnbauer symmetry class DIII, which for both D=2 and D=3 is known to exhibit a stable critical metallic phase. Tensor networks and corresponding random non-unitary circuits in the other nine Altland-Zirnbauer symmetry classes can be obtained from the DIII case by implementing Clifford algebra extensions for classifying spaces.
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