Search

We study the time evolution of long quantum spin chains subjected to continuous monitoring projected on matrix product states (MPS) with fixed bond dimension, by means of the Time-Dependent Variational Principle (TDVP) algorithm. The latter gives an effective unitary evolution which approximates the real quantum evolution up to the projection error. We show that such error displays, at large times, a phase transition in the monitoring strength, which can be well detected by scaling analysis with relatively low values of bond dimensions. Moreover, in the presence of U(1) global spin charge, we show the existence of a charge-sharpening transition well separated from the entanglement transition which we detect by studying the charge fluctuations of a local subpart of the system at large times. Our work shows that quantum monitored dynamics projected on MPS manifolds contains relevant information on measurement-induced phase transitions and provides a new method to identify measured-induced phase transitions in systems of arbitrary dimensions and sizes.

Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-Abelian global symmetry. This work offers a comprehensive group-theoretic account of this elusive phenomenon. For an integrable quantum model with local interactions, invariant under a global non-Abelian simple Lie group G, we find that finite-temperature transport of Noether charges associated with symmetry G in thermal states that are invariant under G is universally superdiffusive and characterized by the dynamical exponent z=3/2. This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: We accordingly dub it “superuniversal.” The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations. We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters. We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua. Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.

We develop a method based on tensor networks to create localized single-particle excitations on top of strongly correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing the gauge freedom of momentum excitations on top of matrix product states. The corresponding wave packets propagate almost dispersionlessly. The time-dependent variational principle is used to scatter two such wave packets, and we extract the phase shift from the collision data. We also study reflection and transmission coefficients of a wave packet impinging on an impurity.