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The importance of the spectral gap in estimating ground-state energies
[article]
2020
arXiv
pre-print
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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- ...
arXiv:2007.11582v1
fatcat:2lqur4xq4zfndnyg6zeglbphka
The Importance of the Spectral Gap in Estimating Ground-State Energies
2022
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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 ...
doi:10.4230/lipics.itcs.2022.54
fatcat:2wdtqif3uncadhvsmk4cd64tty
Undecidability of the spectral gap
2015
Nature
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This is true even with 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. ...
TSC, DPG and MMW thank the Isaac Newton Institute for Mathematical Sciences, Cambridge for their hospitality during the programme "Mathematical Challenges in Quantum Information", where part of this work ...
doi:10.1038/nature16059
pmid:26659181
fatcat:fgk7wqzazvgzrkqk2pomkzsfuu
Energy-gap analysis of quantum spin-glass transitions at zero temperature
2010
Journal of Physics, Conference Series
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2010 pre-print arXiv:1004.2221v1 fatcat:m6rzmn2jljhcjlmuaipwrongsu
We study for random quantum spin systems 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. ...
doi:10.1088/1742-6596/233/1/012008
fatcat:aoawlfli2jhbjj36htyygbpuzq
On physical problems that are slightly more difficult than QMA
[article]
2014
arXiv
pre-print
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computational problems (for example, 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. ...
arXiv:1312.4758v2
fatcat:6kjkq2ngsbespejm3makfy33yy
Electrical Tuning of Exciton Binding Energies in MonolayerWS2
2015
Physical Review Letters
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We demonstrate continuous tuning 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. ...
doi:10.1103/physrevlett.115.126802
pmid:26431003
fatcat:fgyezb6ul5f5lkr5w473kolfre
On the Origin of the Tunneling Asymmetry in the Cuprate Superconductors
[article]
2004
arXiv
pre-print
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We argue this 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. ...
arXiv:cond-mat/0406095v1
fatcat:lwltvddfjvcbtcaqvpdgn7atea
Near-optimal ground state preparation
[article]
2020
arXiv
pre-print
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Preparing 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 ...
arXiv:2002.12508v3
fatcat:u244brlrufgxrozpbpvhenjbwy
Near-optimal ground state preparation
2020
Quantum
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Preparing 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 ...
doi:10.22331/q-2020-12-14-372
fatcat:vrgw75dhhncdvp74ifzx3hchve
Spectral density functions for polyacetylene within the Peierls - Hubbard model
1996
Journal of Physics: Condensed Matter
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We employ 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. ...
doi:10.1088/0953-8984/8/46/006
fatcat:3kdyinw4irdpnev6h7vxfihcvi
Dynamical transition from triplets to spinon excitations: A series expansion study of theJ1−J2−δspin-12chain
1999
Physical Review B (Condensed Matter)
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We then focus on 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. ...
doi:10.1103/physrevb.59.9911
fatcat:4c7jifby3fci5l2ci6vfocyvai
The spectral gap for the ferromagnetic spin-J XXZ chain
2001
Advances in Theoretical and Mathematical Physics
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Our main theorem is that there is a non-vanishing 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. ...
doi:10.4310/atmp.2001.v5.n6.a3
fatcat:a2xzpcpmorevhk3ufh5znp5lhe
Collective Singlet Excitations and Evolution of Raman Spectral Weights in the 2D Spin Dimer CompoundSrCu2(BO3)2
2000
Physical Review Letters
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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] . ...
doi:10.1103/physrevlett.85.2605
pmid:10978118
fatcat:vkuap245w5batpj2olvaqjfi2u
Tunneling density of states, correlation energy, and spin polarization in the fractional quantum Hall regime
[article]
2019
arXiv
pre-print
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We derive exact sum-rules that relate the tunneling density of states (TDOS) of spinful electrons in the fractional quantum Hall (FQH) regime to the spin-dependent many body ground state correlation energy ...
The sum rules can be used to define spin-dependent gaps that we associate with peaks in 2D to 2D tunneling I-V curves. ...
This way it helps extract the important ground state properties of strongly correlated FQH states from tunneling data. ...
arXiv:1811.07203v3
fatcat:4zb37p6yhvavhky4scxt7rbscu
Relating correlation measures: The importance of the energy gap
2017
Physical Review A
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2017 pre-print arXiv:1702.08422v1 fatcat:irfe7l4g5zgwrplafugwxsi65yOther Versions
The key ingredient turns out to be the energy gap within the symmetry-adapted subspace. ...
In quantum chemistry, however, the correlation energy (the energy not seized by the Hartree-Fock ansatz) plays a more prominent role. ...
C.L.B.R. thanks the Clarendon Laboratory at the University of Oxford for the warm hospitality. ...
doi:10.1103/physreva.95.032507
fatcat:wymbkfdsjjfivaxn5gs5p4usrq
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