Area-Law Study of Quantum Spin System on Hyperbolic Lattice Geometries
- URL: http://arxiv.org/abs/2003.10717v1
- Date: Tue, 24 Mar 2020 08:48:36 GMT
- Title: Area-Law Study of Quantum Spin System on Hyperbolic Lattice Geometries
- Authors: Andrej Gendiar
- Abstract summary: Magnetic properties of the transverse-field Ising model on curved (hyperbolic) lattices are studied.
We identify the quantum phase transition for each hyperbolic lattice by calculating the magnetization.
We study the entanglement entropy at the phase transition in order to analyze the correlations of various subsystems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Magnetic properties of the transverse-field Ising model on curved
(hyperbolic) lattices are studied by a tensor product variational formulation
that we have generalized for this purpose. First, we identify the quantum phase
transition for each hyperbolic lattice by calculating the magnetization. We
study the entanglement entropy at the phase transition in order to analyze the
correlations of various subsystems located at the center with the rest of the
lattice. We confirm that the entanglement entropy satisfies the area law at the
phase transition for fixed coordination number, i.e., it scales linearly with
the increasing size of the subsystems. On the other hand, the entanglement
entropy decreases as power-law with respect to the increasing coordination
number.
Related papers
- Volume-law entanglement fragmentation of quasiparticles [0.087024326813104]
We study the entanglement entropy in quasiparticle states where certain unit patterns are excited repeatedly and sequentially in momentum space.
We find that in the scaling limit, each unit pattern contributes independently and universally to the entanglement, leading to a volume-law scaling of the entanglement entropy.
arXiv Detail & Related papers (2024-11-19T09:57:40Z) - Probing quantum floating phases in Rydberg atom arrays [61.242961328078245]
We experimentally observe the emergence of the quantum floating phase in 92 neutral-atom qubits.
The site-resolved measurement reveals the formation of domain walls within the commensurate ordered phase.
As the experimental system sizes increase, we show that the wave vectors approach a continuum of values incommensurate with the lattice.
arXiv Detail & Related papers (2024-01-16T03:26:36Z) - Entanglement entropy of higher rank topological phases [0.0]
We study entanglement entropy of unusual $mathbbZ_N$ topological stabilizer codes which admit fractional excitations with restricted mobility constraint.
It is widely known that the sub-leading term of the entanglement entropy of a disk geometry in conventional topologically ordered phases is related to the total number of the quantum dimension of the fractional excitations.
arXiv Detail & Related papers (2023-02-22T16:06:01Z) - Multipartite Entanglement in the Measurement-Induced Phase Transition of
the Quantum Ising Chain [77.34726150561087]
External monitoring of quantum many-body systems can give rise to a measurement-induced phase transition.
We show that this transition extends beyond bipartite correlations to multipartite entanglement.
arXiv Detail & Related papers (2023-02-13T15:54:11Z) - Topological transitions with continuously monitored free fermions [68.8204255655161]
We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits.
We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
arXiv Detail & Related papers (2021-12-17T22:01:54Z) - Entanglement Transitions from Stochastic Resetting of Non-Hermitian
Quasiparticles [0.0]
We write down a renewal equation for the statistics of the entanglement entropy and show that depending on the spectrum of quasiparticle decay rates different entanglement scaling can arise and even sharp entanglement phase transitions.
When applied to a Quantum Ising chain where the transverse magnetization is measured by quantum jumps, our theory predicts a critical phase with logarithmic scaling of the entanglement, an area law phase and a continuous phase transition between them, with an effective central charge vanishing as a square root at the transition point.
arXiv Detail & Related papers (2021-11-05T13:38:04Z) - Measurement-induced criticality in extended and long-range unitary
circuits [0.0]
We find the range of interactions plays a key role in characterizing both phases and their measurement-induced transitions.
For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy.
In the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions.
arXiv Detail & Related papers (2021-10-27T12:55:07Z) - Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry.
Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
arXiv Detail & Related papers (2021-05-20T14:46:09Z) - Generalized quantum measurements with matrix product states:
Entanglement phase transition and clusterization [58.720142291102135]
We propose a method for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement.
We observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.
arXiv Detail & Related papers (2021-04-21T10:36:57Z) - Determination of the critical exponents in dissipative phase
transitions: Coherent anomaly approach [51.819912248960804]
We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
arXiv Detail & Related papers (2021-03-12T13:16:18Z) - Quantum phase transition of the Bose-Hubbard model on cubic lattice with
anisotropic hopping [7.3711210986071425]
In quantum many-body system, dimensionality plays a critical role on type of the quantum phase transition.
We studied the Bose-Hubbard model on cubic lattice with anisotropic hopping.
arXiv Detail & Related papers (2020-02-25T00:16:48Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.