TY - JOUR
T1 - Quantum spin chains with multiple dynamics
AU - Chen, Xiao
AU - Fradkin, Eduardo
AU - Witczak-Krempa, William
N1 - Funding Information:
We thank A. Ludwig, R. Movassagh, S. Sachdev, M. Stoudenmire, and X. Yu for useful discussions. X.C. was supported by a postdoctoral fellowship from the Gordon and Betty Moore Foundation, under the EPiQS initiative, Grant No. GBMF4304, at the Kavli Institute for Theoretical Physics. This work was supported in part by the U.S. National Science Foundation through Grant No. DMR-1408713 at the University of Illinois (E.F.). W.W.K. was funded by a Discovery Grant from NSERC, and by a Canada Research Chair. The DMRG simulations were performed using the itensor package (version 2). We acknowledge support from the Center for Scientific Computing from the CNSI, MRL, an NSF MRSEC (DMR-1121053).
Publisher Copyright:
© 2017 American Physical Society.
PY - 2017/11/6
Y1 - 2017/11/6
N2 - Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultracold atoms. We investigate such nontrivial quantum dynamics in a different setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled ground state, but a gapless excitation spectrum that is poorly understood. By using large-scale density matrix renormalization group simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2≤z<2.7, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wave function for the ground state, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the nonequilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in two dimensions.
AB - Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultracold atoms. We investigate such nontrivial quantum dynamics in a different setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled ground state, but a gapless excitation spectrum that is poorly understood. By using large-scale density matrix renormalization group simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2≤z<2.7, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wave function for the ground state, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the nonequilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in two dimensions.
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U2 - 10.1103/PhysRevB.96.180402
DO - 10.1103/PhysRevB.96.180402
M3 - Article
AN - SCOPUS:85038829365
SN - 2469-9950
VL - 96
JO - Physical Review B
JF - Physical Review B
IS - 18
M1 - 180402
ER -