Resonating valence bonds and spinon pairing in the Dicke model

Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms coupled to a common photon mode. In the lossy cavity limit, starting with an initial state with MM atoms excited and NN atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an RVB state composed of resonating long-ranged singlets. Each emitted photon reduces the number of singlets by unity, replacing it with a pair of lone spins or ‘spinons’. As spinons are formed coherently in pairs, they are analogous to Cooper pairs in a superconductor. To simulate pair fluctuations, we propose a protocol in which photons are allowed to escape the cavity undetected. This leads to an inchoate superconductor – mixed quantum state with a fluctuating number of spinon pairs. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization, the emission exhibits a continuous transition from a dark state to a bright state. This opens an exciting route to simulate RVB states and superconductivity.

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TWO-DIMENSIONAL ANTIFERROMAGNETIC HEISENBERG MODEL: EXACT AND RVB STATES

International Journal of Modern Physics B ◽

10.1142/s0217979288000810 ◽

1988 ◽

Vol 02 (05) ◽

pp. 981-992 ◽

Cited By ~ 1

Author(s):

D. Poilblanc

Keyword(s):

Ground State ◽

Heisenberg Model ◽

State Energy ◽

Group Representation ◽

Valence Bond ◽

Periodic Boundary Conditions ◽

Energy Functional ◽

Many Body ◽

Real Numbers ◽

Wave Symmetry

The exact many-body states of a 10-site square cluster with periodic boundary conditions of a S = 1/2 antiferromagnetic Heisenberg lattice model are investigated. A general form of a Resonating Valence Bond wavefunction (RVB), written in fermion representation is examined. It is shown that the optimum variational wavefunction has complex singlet bond distribution amplitudes of s+id symmetry . It has a very large overlap with the groundstate, belongs to the same space group representation and its energy functional has a minimum very close to the ground-state energy. On the other hand, if the amplitudes are restricted to real numbers, the local minimum has slightly higher energy and d-wave symmetry.

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REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

International Journal of Modern Physics E ◽

10.1142/s021830130801194x ◽

2008 ◽

Vol 17 (supp01) ◽

pp. 304-317

Author(s):

Y. M. ZHAO

Keyword(s):

Ground State ◽

Collective Motion ◽

Regular Structure ◽

Positive Parity ◽

Many Body ◽

Random Interactions ◽

Atomic Nuclei ◽

Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

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Spin-one dark matter and gamma ray signals from the galactic center

Journal of High Energy Physics ◽

10.1007/jhep08(2020)106 ◽

2020 ◽

Vol 2020 (8) ◽

Author(s):

H. Hernández-Arellano ◽

M. Napsuciale ◽

S. Rodríguez

Keyword(s):

Dark Matter ◽

Cross Section ◽

Gamma Ray ◽

Galactic Center ◽

Photon Emission ◽

Scalar Coupling ◽

Initial State ◽

Internal Bremsstrahlung ◽

Resonance Effects ◽

State Radiation

Abstract In this work we study the possibility that the gamma ray excess (GRE) at the Milky Way galactic center come from the annihilation of dark matter with a (1, 0) ⊕ (0, 1) space-time structure (spin-one dark matter, SODM). We calculate the production of prompt photons from initial state radiation, internal bremsstrahlung, final state radiation including the emission from the decay products of the μ, τ or hadronization of quarks. Next we study the delayed photon emission from the inverse Compton scattering (ICS) of electrons (produced directly or in the prompt decay of μ, τ leptons or in the hadronization of quarks produced in the annihilation of SODM) with the cosmic microwave background or starlight. All these mechanisms yield significant contributions only for Higgs resonant exchange, i.e. for M ≈ MH /2, and the results depend on the Higgs scalar coupling to SODM, gs. The dominant mechanism at the GRE bump is the prompt photon production in the hadronization of b quarks produced in $$ \overline{D}D\to \overline{b}b $$ D ¯ D → b ¯ b , whereas the delayed photon emission from the ICS of electrons coming from the hadronization of b quarks produced in the same reaction dominates at low energies (ω < 0.3 GeV ) and prompt photons from c and τ , as well as from internal bremsstrahlung, yield competitive contributions at the end point of the spectrum (ω ≥ 30 GeV ). Taking into account all these contributions, our results for photons produced in the annihilation of SODM are in good agreement with the GRE data for gs ∈ [0.98, 1.01] × 10−3 and M ∈ [62.470, 62.505] GeV . We study the consistency of the corresponding results for the dark matter relic density, the spin-independent dark matter-nucleon cross-section σp and the cross section for the annihilation of dark matter into $$ \overline{b}b $$ b ¯ b , τ+τ−, μ+μ− and γγ, taking into account the Higgs resonance effects, finding consistent results in all cases.

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Probing resonating valence bond states in artificial quantum magnets

Nature Communications ◽

10.1038/s41467-021-21274-5 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Kai Yang ◽

Soo-Hyon Phark ◽

Yujeong Bae ◽

Taner Esat ◽

Philip Willke ◽

...

Keyword(s):

Quantum Information Processing ◽

Energy Levels ◽

Finite Size ◽

Valence Bond ◽

Exchange Interactions ◽

Atomic Scale ◽

Scanning Tunneling ◽

Many Body ◽

Quantum Magnets ◽

Resonating Valence Bond

AbstractDesigning and characterizing the many-body behaviors of quantum materials represents a prominent challenge for understanding strongly correlated physics and quantum information processing. We constructed artificial quantum magnets on a surface by using spin-1/2 atoms in a scanning tunneling microscope (STM). These coupled spins feature strong quantum fluctuations due to antiferromagnetic exchange interactions between neighboring atoms. To characterize the resulting collective magnetic states and their energy levels, we performed electron spin resonance on individual atoms within each quantum magnet. This gives atomic-scale access to properties of the exotic quantum many-body states, such as a finite-size realization of a resonating valence bond state. The tunable atomic-scale magnetic field from the STM tip allows us to further characterize and engineer the quantum states. These results open a new avenue to designing and exploring quantum magnets at the atomic scale for applications in spintronics and quantum simulations.

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Undecidability in quantum thermalization

Nature Communications ◽

10.1038/s41467-021-25053-0 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Naoto Shiraishi ◽

Keiji Matsumoto

Keyword(s):

Turing Machine ◽

Thermal Equilibrium ◽

General Theorem ◽

Nearest Neighbour ◽

Many Body ◽

Initial State ◽

One Dimensional ◽

Universal Turing Machine ◽

Many Body Systems ◽

Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

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Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽

10.3390/e22090984 ◽

2020 ◽

Vol 22 (9) ◽

pp. 984

Author(s):

Regina Finsterhölzl ◽

Manuel Katzer ◽

Andreas Knorr ◽

Alexander Carmele

Keyword(s):

Time Evolution ◽

Nearest Neighbor ◽

Matrix Product ◽

Body System ◽

Many Body ◽

Initial State ◽

Matrix Product States ◽

Open Quantum ◽

Many Body Systems ◽

The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

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0+Ground State Dominance in Many-Body Systems

Progress of Theoretical Physics Supplement ◽

10.1143/ptps.146.644 ◽

2002 ◽

Vol 146 ◽

pp. 644-645

Author(s):

Yu-Min Zhao ◽

Akito Arima ◽

Naotaka Yoshinaga

Keyword(s):

Ground State ◽

Many Body ◽

Many Body Systems

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THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

International Journal of Modern Physics B ◽

10.1142/s0217979207043592 ◽

2007 ◽

Vol 21 (13n14) ◽

pp. 2204-2214 ◽

Cited By ~ 7

Author(s):

BEATE PAULUS

Keyword(s):

Experimental Data ◽

Ab Initio ◽

Ground State ◽

Infinite System ◽

Correlation Energy ◽

Correlation Method ◽

Many Body ◽

Hartree Fock ◽

The Many ◽

Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

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