Area-law entanglement from quantum geometry
- URL: http://arxiv.org/abs/2210.13502v1
- Date: Mon, 24 Oct 2022 18:00:59 GMT
- Title: Area-law entanglement from quantum geometry
- Authors: Nisarga Paul
- Abstract summary: We study the entanglement entropy of a region of linear size $ell$ in fermion systems with nontrivial quantum geometry.
We show that the entanglement entropy scales as $S = alpha elld-1 lnell + beta elld-1 + cdots$ where the first term is the well-known area-law violating term for fermions.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum geometry, which encompasses both Berry curvature and the quantum
metric, plays a key role in multi-band interacting electron systems. We study
the entanglement entropy of a region of linear size $\ell$ in fermion systems
with nontrivial quantum geometry, i.e. whose Bloch states have nontrivial $k$
dependence. We show that the entanglement entropy scales as $S = \alpha
\ell^{d-1} \ln\ell + \beta \ell^{d-1} + \cdots$ where the first term is the
well-known area-law violating term for fermions and $\beta$ contains the
leading contribution from quantum geometry. We compute this for the case of
uniform quantum geometry and cubic domains and provide numerical results for
the Su-Schrieffer-Heeger model, 2D massive Dirac cone, and 2D Chern bands. An
experimental probe of the quantum geometric entanglement entropy is proposed
using particle number fluctuations. We offer an intuitive account of the
area-law entanglement related to the spread of maximally localized Wannier
functions.
Related papers
- Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms [0.0]
We study the ability of quantum algorithms to prepare ground states in a matter-free non-Abelian $SO(3)$ lattice gauge theory in $2+1$D.
To deal with the large Hilbert space of gauge fields, we demonstrate how the exact imposition of the non-Abelian Gauss Law in the rishon representation of the quantum link operator significantly reduces the degrees of freedom.
arXiv Detail & Related papers (2024-09-11T08:55:59Z) - Analog Quantum Simulator of a Quantum Field Theory with Fermion-Spin Systems in Silicon [34.80375275076655]
Mapping fermions to qubits is challenging in $2+1$ and higher spacetime dimensions.
We propose a native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays in silicon.
arXiv Detail & Related papers (2024-07-03T18:00:52Z) - Symmetry: a fundamental resource for quantum coherence and metrology [0.0]
We show that when the quantum state is an eigenstate of an operator $A$, observables $G$ which are completely off-diagonal have purely quantum fluctuations.
This property holds regardless of the purity of the quantum state, and it implies that off-diagonal fluctuations represent a metrological resource for phase estimation.
arXiv Detail & Related papers (2024-07-01T07:19:37Z) - Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
We show how to reduce the geometry of degenerate states to the non-abelian connection $A$.
We find independent invariants associated with each triple of subspaces.
Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
arXiv Detail & Related papers (2024-04-04T06:39:28Z) - Entanglement Entropy of ($\mathbf{2+1}$)-Dimensional SU(2) Lattice Gauge Theory on Plaquette Chains [0.5592394503914488]
We study the entanglement entropy of Hamiltonian SU(2) lattice gauge theory in $2+1$ dimensions on linear plaquette chains.
Quantum many-body scars in the middle of the spectrum, which are present in the electric flux truncated Hilbert space, disappear when higher electric field representations are included in the Hilbert space basis.
arXiv Detail & Related papers (2024-01-26T20:05:15Z) - Orthonormal bases of extreme quantumness [1.1510009152620668]
Some coherent and anticoherent spin states are known as optimal quantum rotosensors.
We introduce a measure of quantumness for orthonormal bases of spin states, determined by the average anticoherence of individual vectors and the Wehrl entropy.
arXiv Detail & Related papers (2023-06-01T10:35:45Z) - Theory of free fermions under random projective measurements [43.04146484262759]
We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers.
We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
arXiv Detail & Related papers (2023-04-06T15:19:33Z) - The Wasserstein distance of order 1 for quantum spin systems on infinite
lattices [13.452510519858995]
We show a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice $mathbbZd$.
We also prove that local quantum commuting interactions above a critical temperature satisfy a transportation-cost inequality.
arXiv Detail & Related papers (2022-10-20T17:46:18Z) - Speeding up Learning Quantum States through Group Equivariant
Convolutional Quantum Ans\"atze [13.651587339535961]
We develop a framework for convolutional quantum circuits with SU$(d)$symmetry.
We prove Harrow's statement on equivalence between $nameSU(d)$ and $S_n$ irrep bases.
arXiv Detail & Related papers (2021-12-14T18:03:43Z) - Towards the continuum limit of a $(1+1)$d quantum link Schwinger model [0.0]
We show the continuum limit for gauge theories regularized via finite-dimensional Hilbert spaces of quantum spin-$S$ operators.
Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.
arXiv Detail & Related papers (2021-03-31T18:00:13Z) - Improved thermal area law and quasi-linear time algorithm for quantum
Gibbs states [14.567067583556714]
We propose a new thermal area law that holds for generic many-body systems on lattices.
We improve the temperature dependence from the original $mathcalO(beta)$ to $tildemathcalO(beta2/3)$.
We also prove analogous bounds for the R'enyi entanglement of purification and the entanglement of formation.
arXiv Detail & Related papers (2020-07-22T02:55:27Z)
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.