The authors explore critical properties of entanglement phase transitions in random tensor networks and monitored quantum circuits with Clifford tensors/gates for on-site Hilbert space dimensions which are powers of a prime number
p. Exact mappings to replica spin models and characterizations of their symmetry groups predict that all universal properties will depend only on
p. These predictions are confirmed with extensive numerical simulations. The authors also establish multifractal scaling of the purity, reflected in a continuous spectrum of critical exponents, while the typical exponent is the prefactor of the logarithm in the entanglement entropy.
A new class of quantum entanglement transitions separating phases with different entanglement entropy scaling has been observed in recent numerical studies. Despite the numerical efforts, an analytical understanding of such transitions has remained elusive. Here, the authors propose a theory for the area-law to volume-law entanglement transition in many-body systems that undergo both random unitary evolutions and projective measurements. Using the replica method, the authors map analytically this entanglement transition to an ordering transition in a classical statistical mechanics model. They derive the general entanglement scaling properties at the transition and show a solvable limit where this transition can be mapped onto two-dimensional percolation.
Entanglement transitions in quantum dynamics present a novel class of phase transitions in non-equilibrium systems. When a many-body quantum system undergoes hybrid quantum dynamics, consisting of unitary evolution interspersed with monitored random measurements, the steady-state can exhibit a phase transition between volume- and area-law entanglement. The role of dimension in the nature of these transitions is an open problem. There is a dimensional correspondence between measurement-induced transitions in non-unitary quantum circuits in
d spatial dimensions and classical statistical mechanical models in
d+1 dimensions, where the time dimension in the quantum problem is mapped to a spatial dimension in the classical model. In this work we show that the role of dimension is considerably richer by unveiling a form of `dimensional hybridity': critical properties of the steady-state entanglement are governed by a combination of exponents consistent with
d-dimensional percolation and
(d+1)-dimensional percolation. We uncover this dimensional hybridity in 1+1D and 2+1D circuits using a graph-state based simulation algorithm where the entanglement structure is encoded in an underlying graph, providing access to the geometric structure of entanglement. We locate the critical point using the tripartite information, revealing area-law entanglement scaling at criticality, and showing that the entanglement transition coincides with the purification transition. The emergence of this `dimensional hybridity' in these non-unitary quantum circuits sheds new light on the universality of measurement-induced transitions, and opens the way for analyzing the quantum error correcting properties of random unitary circuits in higher dimensions.
Spin-liquid and spin-glass states represent two distinct phases of disordered quantum spin systems. These states are, in principle, distinguished by quantum-entangled fluctuations and spin freezing, but identifying each state and characterizing the transition between them remains challenging. Here, we systematically explore the relationship between the spin-liquid and spin-glass states using a model with all-to-all random interactions among
p spins, which interpolates between the Ising-like one-component, XY-like two-component, and isotropic three-component cases. By analyzing the system-size
N dependence of the Edwards-Anderson order parameter and the density of states, we identify the transition from the spin liquid to the spin glass for various values of
p. We show that the phase diagrams for different
p can be unified through a scaling with
N/p2, revealing that increasing anisotropy in the interactions systematically suppresses the spin-liquid phase and extends the spin-glass regime. Furthermore, we examine the competition between multiple-spin interactions and anisotropy under an external magnetic field in the isotropic case, and find that the spin-liquid phase transitions into the spin-glass phase before entering a quantum paramagnetic phase. Our findings provide insights into quantum disordered phases and the transitions between them.
We introduce a class of hybrid quantum circuits, with random unitaries and projective measurements, which host long-range order in the area-law entanglement phase of the steady state.Our primary example is circuits with unitaries respecting a global Ising symmetry and two competing types of measurements.The phase diagram has an area-law phase with spin-glass order, which undergoes a direct transition to a paramagnetic phase with volume-law entanglement, as well as a critical regime.Using mutual information diagnostics, we find that such entanglement transitions preserving a global symmetry are in universality classes different from those without symmetry.We analyze generalizations of such hybrid circuits to higher dimensions, which allow for coexistence of order and volume-law entanglement, as well as topological order without any symmetry restrictions.
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.