Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models

@article{Mark2020UnifiedSF,
  title={Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models},
  author={Daniel K. Mark and Cheng-Ju Lin and Olexei I. Motrunich},
  journal={Physical Review B},
  year={2020},
  volume={101},
  pages={195131}
}
Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed “towers” of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT and spin-1 XY models, and a spin-1/2 model that conserves the number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the… 

Figures from this paper

Quantum Many-Body Scars: A Quasiparticle Perspective
Weakly interacting quasiparticles play a central role in the low-energy description of many phases of quantum matter. At higher energies, however, quasiparticles cease to be well-defined in generic
Tuning between continuous time crystals and many-body scars in long-range XYZ spin chains
Persistent oscillatory dynamics in non-equilibrium many-body systems is a tantalizing manifesta-tion of ergodicity breakdown that continues to attract much attention. Recent works have focused on two
Bridging quantum many-body scar and quantum integrability in Ising chains with transverse and longitudinal fields
Quantum many-body scar (QMBS) and quantum integrability(QI) have been recognized as two distinct mechanisms for the breakdown of eigenstate thermalization hypothesis(ETH) in an isolated system. In
Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability
We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the η -pairing mechanism. Our models include the SU( N ) Hubbard model as a special case.
Integrable quantum many-body scars in a non-integrable large-N spin chain
Exact quantum many-body scar states in non-integrable models that have been found in recent years all share the common property of being lowly entangled, therefore representable by matrix product
Quantum many-body scars beyond single mode approximation
Since its experimental discovery, quantum many-body scar states, both in the form of approxi-mate numerical and exact analytical solutions, have always been closely related to momentum π . While
Stabilizing Gauge Theories in Quantum Simulators: A Brief Review
Quantum simulation is at the heart of the ongoing “second” quantum revolution, with various synthetic quantum matter platforms realizing evermore exotic condensed matter and particle physics
Driving quantum many-body scars
Periodic driving has been established as a powerful technique for engineering novel phases of matter and intrinsically out-of-equilibrium phenomena such as time crystals. Recent work by Bluvstein et
Prominent quantum many-body scars in a truncated Schwinger model
The high level of control and precision achievable in current synthetic quantum matter setups has enabled first attempts at quantum-simulating various intriguing phenomena in condensed matter physics,
Weak Ergodicity Breaking in the Schwinger Model
As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been
...
...

References

SHOWING 1-10 OF 113 REFERENCES
Europhys
  • Lett. 24, 293
  • 1993
Phys
  • Rev. B 98, 235155
  • 2018
Phys
  • Rev. Lett. 123, 147201
  • 2019
Phys
  • Rev. Lett. 59, 799
  • 1987
Quantum scars as embeddings of weakly broken Lie algebra representations
Recently, much effort has focused on understanding weak ergodicity breaking in many-body quantum systems that could lead to wavefunction revivals in their dynamics far from equilibrium. An example of
Onsager's Scars in Disordered Spin Chains.
TLDR
This model is the first explicit example of disordered quantum many-body scarred models and clearly shows that the scar states are trapped in a perfectly periodic orbit in the Hilbert subspace and never thermalize, whereas other generic states do rapidly.
and s
Revivals imply quantum many-body scars
We derive general results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites
Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals
Strongly interacting systems with quantum many-body scars exhibit persistent fidelity oscillations when prepared in a certain class of initial states, but otherwise undergo ergodic dynamics. Previous
Confined Phases of One-Dimensional Spinless Fermions Coupled to Z_{2} Gauge Theory.
TLDR
This work investigates a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field and develops an exactly solvable effective theory of bosonic dimers with emergent constraints at strong coupling.
...
...