Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

by Samudra Sur (ILSc Bangalore)

Thursday 14 Sept 2023, 14:00 → 15:00 Europe/Zurich

WHGA/121

We study a one-dimensional spin-1/2 model with three-spin interactions and a transverse magnetic field h. The model is known to have a Z_2 \times Z_2 symmetry, and a duality between h and 1/h. The self-dual point at h=1 is a quantum critical point with a continuous phase transition. We compute the critical exponents z, \beta, \gamma and \nu, and the central charge c numerically using exact diagonalization. We find that both z and c are equal to 1, implying that the critical point is governed by a conformal field theory with a marginal operator. The three-spin model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between four-state Potts model and two decoupled transverse field Ising models. An energy level spacing analysis shows that the model is not integrable. For a system with an even number of sites and periodic boundary conditions, there are exact mid-spectrum zero-energy eigenstates whose number grows exponentially with the system size. A subset of these eigenstates have wave functions which are independent of the value of h and have unusual entanglement structure; hence these can be considered to be quantum many-body scars. The number of such quantum scars scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions at sites close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if h \gg 1 or h \ll 1. If h is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.