Related Experiment Video
Updated: May 9, 2026
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Entanglement spectrum of the two-dimensional Bose-Hubbard model
Vincenzo Alba1, Masudul Haque, Andreas M Läuchli
1Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, D-80333 München, Germany.
Physical Review Letters
|July 16, 2013
Summary
We investigated the entanglement spectrum (ES) of the Bose-Hubbard model in Mott insulating and superfluid phases. The ES reveals boundary physics in the Mott phase and broken U(1) symmetry in the superfluid phase.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
Background:
- The Bose-Hubbard model describes interacting bosons on a lattice, crucial for understanding quantum phases like Mott insulators and superfluids.
- Entanglement spectrum (ES) provides insights into the topological and symmetry properties of quantum many-body systems.
Purpose of the Study:
- To analyze the entanglement spectrum (ES) of the 2D Bose-Hubbard model at unit filling.
- To understand how ES reflects distinct quantum phases (Mott insulator, superfluid) and their transition.
- To explore the implications of ES structure on entanglement entropy and computational algorithms.
Main Methods:
- Numerical study of the Bose-Hubbard model on a 2D square lattice.
- Analysis of the entanglement spectrum (ES) in both Mott insulating and superfluid phases.
- Investigation of ES evolution across the quantum phase transition.
Main Results:
- In the Mott phase, ES is dominated by boundary physics, with 1D dispersion effects.
- In the superfluid phase, ES reflects broken U(1) symmetry and exhibits a 'tower of states' structure.
- Characteristic ES structures evolve across the superfluid-Mott insulator transition, impacting entanglement entropy.
Conclusions:
- The entanglement spectrum (ES) offers a powerful tool to characterize quantum phases and transitions in the Bose-Hubbard model.
- ES structure provides insights into symmetry breaking and boundary effects.
- Understanding ES is crucial for developing efficient quantum simulation algorithms, particularly matrix-product-state methods.
Related Concept Videos
01:18Structure of Benzene: Molecular Orbital Model
According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).
01:08Spin–Spin Coupling Constant: Overview
In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
01:192D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)
Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
02:18The Bohr Model
Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus...
02:45The Quantum-Mechanical Model of an Atom
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...