UC Berkeley

Non-equilibrium properties of quantum materials are examined in low-dimensional systems using matrix product state (MPS) simulations. The spectral function known as the dynamical structure factor, which is directly observed in neutron scattering experiments, is studied for two classes of novel quantum systems. First, recent work has demonstrated that the Heisenberg spin chain exhibits anomalous super-diffusive transport at infinite temperature called Kardar-Parisi-Zhang (KPZ) hydrodynamics. Here, it is demonstrated that signatures of KPZ physics are present in the low-energy spectrum at experimentally relevant temperatures, and this has been detected in KCuF_3 with neutron scattering. The crossover from the ground state physics described by the Tomonaga-Luttinger liquid theory to KPZ hydrodynamics at high temperatures is explored.

Second, the spectral function of the J_1-J_2 Heisenberg model is studied using MPS simulations. Signatures for the three primary classes of quantum spin liquid (QSL) states in the spectral function are discussed. Our findings point to a U(1) Dirac spin liquid ground state in this model. The calculated spectrum is then compared with the triangluar lattice compounds KYbSe_2 and YbZn_2GaO_5. We find that KYbSe_2 is well modelled by the J_1-J_2 Heisenberg model in close proximity to the QSL phase. Additionally, we find that the QSL phase of the J_1-J_2 Heisenberg model captures the essential features of the YbZn_2GaO_5, suggesting a realization of a Dirac spin liquid in this material.

Lastly, the effect of using an MPS to study quantum dynamics is explored. Using an MPS places a restriction on the entanglement in the system, and we study how this modifies time dynamics in a Kibble-Zurek process.We derive that the effect of finite entanglement on a Kibble-Zurek process is captured by a dimensionless scaling function of the ratio of two length scales, one determined dynamically and one by the entanglement restriction. This result is verified numerically in the transverse field Ising model and the 3-state Potts model.