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The importance of the spectral gap in estimating ground-state energies
[article]

2020
*
arXiv
*
pre-print

*In*this work, we make progress on this question by considering

*the*precise regime,

*in*which one

*estimates*

*the*

*ground*-

*state*

*energy*to within inverse exponential precision. ... Despite its

*importance*

*in*quantum many-body physics,

*the*role played by

*the*

*spectral*

*gap*

*in*

*the*complexity

*of*

*the*LocalHamiltonian is less well-understood. ... We thank an anonymous referee

*of*an earlier version

*of*this manuscript for pointing out

*the*similarity

*of*imaginary-time evolution with

*the*power method and Cedric Lin for show- ...

##
###
The Importance of the Spectral Gap in Estimating Ground-State Energies

2022

*In*this work, we make progress on this question by considering

*the*precise regime,

*in*which one

*estimates*

*the*

*ground*-

*state*

*energy*to within inverse exponential precision. ... Despite its

*importance*

*in*quantum many-body physics,

*the*role played by

*the*

*spectral*

*gap*

*in*

*the*complexity

*of*

*the*Local Hamiltonian problem is less well-understood. ... I T C S 2 0 2 2 54:4

*The*

*Importance*

*of*

*the*

*Spectral*

*Gap*

*in*

*Estimating*

*Ground*-

*State*

*Energies*

*In*

*the*regime

*of*inverse-exponential precision, our work explains a seemingly puzzling fact, namely

*the*PSPACE-completeness ...

##
###
Energy-gap analysis of quantum spin-glass transitions at zero temperature

2010
*
Journal of Physics, Conference Series
*

We study for random quantum spin systems

doi:10.1088/1742-6596/233/1/012008
fatcat:aoawlfli2jhbjj36htyygbpuzq
*the**energy**gap*between*the**ground*and first excited*states*to clarify a relation to*the*spin-glass-paramagnetic phase transition. ... On*the*other hand,*the*classical treatment is justified for*the*transverse random*energy*model and*the*phase transition can be found by a sudden change*of**the**ground**state*. ... Y.M. acknowledges support from*the*Japan Society for*the*Promotion*of*Science. ...##
###
On physical problems that are slightly more difficult than QMA
[article]

2014
*
arXiv
*
pre-print

computational problems (for example,

arXiv:1312.4758v2
fatcat:6kjkq2ngsbespejm3makfy33yy
*the*complexity*of**estimating**the**spectral**gap**of*a Hamiltonian). ... We study*the*complexity*of*computational problems from quantum physics. ... Any opinions, findings and conclusions or recommendations expressed*in*this material are those*of**the*author(s) and do not necessarily reflect*the*views*of**the*National Science Foundation. ...##
###
Electrical Tuning of Exciton Binding Energies in MonolayerWS2

2015
*
Physical Review Letters
*

We demonstrate continuous tuning

doi:10.1103/physrevlett.115.126802
pmid:26431003
fatcat:fgyezb6ul5f5lkr5w473kolfre
*of**the*exciton binding*energy**in*monolayer WS 2 by means*of*an externally applied voltage*in*a field-effect transistor device. ... Using optical spectroscopy, we monitor theground and excited excitonic*states*as a function*of*gate voltage and track*the*evolution*of**the*quasiparticle band*gap*. ...*The*authors would like to thank Timothy C. Berkelbach A. C. and A. M. vdZ. contributed equally to this work. ...##
###
Near-optimal ground state preparation
[article]

2020
*
arXiv
*
pre-print

Preparing

arXiv:2002.12508v3
fatcat:u244brlrufgxrozpbpvhenjbwy
*the**ground**state**of*a given Hamiltonian and*estimating*its*ground**energy*are*important*but computationally hard tasks. ... We assume that an initial*state*with non-trivial overlap with*the**ground**state*can be efficiently prepared, and*the**spectral**gap*between*the**ground**energy*and*the*first excited*energy*is bounded from below ... Introduction*Estimating**ground**energy*and obtaining information on*the**ground**state**of*a given quantum Hamiltonian are*of*immense*importance**in*condensed matter physics, quantum chemistry, and quantum ...##
###
Near-optimal ground state preparation

2020
*
Quantum
*

Preparing

doi:10.22331/q-2020-12-14-372
fatcat:vrgw75dhhncdvp74ifzx3hchve
*the**ground**state**of*a given Hamiltonian and*estimating*its*ground**energy*are*important*but computationally hard tasks. ... We assume that an initial*state*with non-trivial overlap with*the**ground**state*can be efficiently prepared, and*the**spectral**gap*between*the**ground**energy*and*the*first excited*energy*is bounded from below ... Introduction*Estimating**ground**energy*and obtaining information on*the**ground**state**of*a given quantum Hamiltonian are*of*immense*importance**in*condensed matter physics, quantum chemistry, and quantum ...##
###
On the Origin of the Tunneling Asymmetry in the Cuprate Superconductors
[article]

2004
*
arXiv
*
pre-print

We argue this

arXiv:cond-mat/0406095v1
fatcat:lwltvddfjvcbtcaqvpdgn7atea
*gap*may represent a new*energy*scale*of**the*system, namely*the**energy*scale for spin-charge recombination*in*this system. ... We argue*the*coherent part*of**the**spectral*weight always contribute symmetrically to*the*STM spectrum at sufficiently low*energy*and*the*tunneling asymmetry is a manifestation*of**the*incoherent part*of*...*In**the*system studied,*the**energy**of**the*neutron resonance mode E r can be*estimated*from*the*T c − E r scaling to be E r ∼ 37 meV. ...##
###
Spectral density functions for polyacetylene within the Peierls - Hubbard model

1996
*
Journal of Physics: Condensed Matter
*

We employ

doi:10.1088/0953-8984/8/46/006
fatcat:3kdyinw4irdpnev6h7vxfihcvi
*the*Lanczos method to calculate*the**ground*-*state*properties and single-particle*spectral*density functions appropriate for*the*description*of**the*photoemission and*the*inverse photoemission spectra ... Three*of**the*four carbon valence electrons participate*in*σ -bonds, while one electron participates*in**the*π-bond (sp 2 hybridization). Electronic*energies**of*σ -bonds are at relatively deep levels. ... This work was supported by*the*Committee*of*Scientific Research (KBN) Project No 2PO3B 144 08. ...##
###
Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm
[article]

2022
*
arXiv
*
pre-print

*The*adiabatic algorithm is known to return

*the*

*ground*

*state*for sufficiently long preparation times which depend on

*the*a priori unknown

*spectral*

*gap*. Our work relates

*in*a twofold way. ... Preparing

*the*

*ground*

*state*

*of*a Hamiltonian is a problem

*of*great significance

*in*physics with deep implications

*in*

*the*field

*of*combinatorial optimization. ...

*the*project number 414325145

*in*

*the*framework

*of*

*the*Austrian Science Fund (FWF): SFB F7104. ...

##
###
Dynamical transition from triplets to spinon excitations: A series expansion study of theJ1−J2−δspin-12chain

1999
*
Physical Review B (Condensed Matter)
*

We then focus on

doi:10.1103/physrevb.59.9911
fatcat:4c7jifby3fci5l2ci6vfocyvai
*the*disorder line y=0.5, 0<δ< 1, where*the**ground**states*are known exactly. ...*In*particular, we show that*the**spectral*weight for*the*triplets vanishes and*the*static spin-susceptibility changes from a simple pole at imaginary wavevectors to a branch cut at*the*transition. ... Part*of**the*computation*in*this work has been done using*the*facilities*of**the*New South Wales Centre for Parallel Computing. ...##
###
The spectral gap for the ferromagnetic spin-J XXZ chain

2001
*
Advances in Theoretical and Mathematical Physics
*

Our main theorem is that there is a non-vanishing

doi:10.4310/atmp.2001.v5.n6.a3
fatcat:a2xzpcpmorevhk3ufh5znp5lhe
*gap*above all*ground**states**of*this model for all values*of*J. ...*state*, about*the*scaling*of**the**gap*and*the*structure*of**the*low-lying spectrum for large J, and about*the*existence*of*isolated eigenvalues*in**the*excitation spectrum. e-print archive: http://xxx.lanLgov ... However,*the*low*energy**states*may be more*important*for dynamical properties (cf [9] ), since that part*of**the*spectrum is separated by*spectral**gaps*. ...##
###
Minimal action control method in quantum critical models
[article]

2022
*
arXiv
*
pre-print

and requires only a reasonable approximation for

arXiv:2208.09271v1
fatcat:wkp4ybanhvgsth25oxslwqgop4
*the**ground**state**spectral**gap*. ... Using tools based on*the*geometry*of*quantum evolutions through*the*quantum adiabatic brachistochrone, we show that high fidelity control*of**the**ground**state**of*critical quantum systems can be achieved ... ACKNOWLEDGMENTS This work is supported by*the*Science Foundation Ireland Starting Investigator Research Grant "SpeedDemon" No. 18/SIRG/5508. ...##
###
Undecidability of the spectral gap

2015
*
Nature
*

This is true even with

doi:10.1038/nature16059
pmid:26659181
fatcat:fgk7wqzazvgzrkqk2pomkzsfuu
*the*promise that each Hamiltonian is either*gapped*or gapless*in**the*strongest sense: it is promised to either have continuous spectrum above*the**ground**state**in**the*thermodynamic ... limit, or its*spectral**gap*is lower-bounded by a constant*in**the*thermodynamic limit. ...*The*most*important*step*in*proving undecidability*of**the**spectral**gap*is to prove undecidability*of*another relevant quantity:*the**ground**state**energy*density. ...##
###
Collective Singlet Excitations and Evolution of Raman Spectral Weights in the 2D Spin Dimer CompoundSrCu2(BO3)2

2000
*
Physical Review Letters
*

*The*key to

*the*understanding

*of*

*the*unique features

*of*SrCu2(BO3)2 is

*the*presence

*of*strong interactions between well-localized triplet excitations

*in*

*the*network

*of*orthogonal spin dimers realized

*in*... Based on our analysis

*of*

*the*Heisenberg model relevant for this material, we argue that

*the*collective excitations involving two and three-particle singlet bound

*states*have large binding

*energies*and ... Thermodynamic measurements support

*the*existence

*of*a dimer

*ground*

*state*and a spin

*gap*

*of*D 34 K [1, 6] . ...

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