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

Abhinav Deshpande, Alexey V. Gorshkov, Bill Fefferman
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-  ... 
arXiv:2007.11582v1 fatcat:2lqur4xq4zfndnyg6zeglbphka

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

Abhinav Deshpande, Alexey V. Gorshkov, Bill Fefferman, Mark Braverman
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  ... 
doi:10.4230/lipics.itcs.2022.54 fatcat:2wdtqif3uncadhvsmk4cd64tty

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

Kazutaka Takahashi, Yoshiki Matsuda
2010 Journal of Physics, Conference Series  
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]

Andris Ambainis
2014 arXiv   pre-print
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

Alexey Chernikov, Arend M. van der Zande, Heather M. Hill, Albert F. Rigosi, Ajanth Velauthapillai, James Hone, Tony F. Heinz
2015 Physical Review Letters  
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

Near-optimal ground state preparation [article]

Lin Lin, Yu Tong
2020 arXiv   pre-print
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

Lin Lin, Yu Tong
2020 Quantum  
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

On the Origin of the Tunneling Asymmetry in the Cuprate Superconductors [article]

Tao Li, Fan Yang, Yong-Jin Jiang
2004 arXiv   pre-print
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

Spectral density functions for polyacetylene within the Peierls - Hubbard model

D Góra, K Rosciszewski
1996 Journal of Physics: Condensed Matter  
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

Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm [article]

Benjamin F. Schiffer, Jordi Tura, J. Ignacio Cirac
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.  ... 
arXiv:2103.01226v2 fatcat:2i5mz3fpd5h4hntyhwdqgqcbv4

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

Rajiv R. P. Singh, Zheng Weihong
1999 Physical Review B (Condensed Matter)  
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

Tohru Koma, Bruno Nachtergaele, Shannon Starr
2001 Advances in Theoretical and Mathematical Physics  
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

Minimal action control method in quantum critical models [article]

Ainur Kazhybekova, Steve Campbell, Anthony Kiely
2022 arXiv   pre-print
and requires only a reasonable approximation for 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.  ... 
arXiv:2208.09271v1 fatcat:wkp4ybanhvgsth25oxslwqgop4

Undecidability of the spectral gap

Toby S. Cubitt, David Perez-Garcia, Michael M. Wolf
2015 Nature  
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.  ...  The most important step in proving undecidability of the spectral gap is to prove undecidability of another relevant quantity: the ground state energy density.  ... 
doi:10.1038/nature16059 pmid:26659181 fatcat:fgk7wqzazvgzrkqk2pomkzsfuu

Collective Singlet Excitations and Evolution of Raman Spectral Weights in the 2D Spin Dimer CompoundSrCu2(BO3)2

P. Lemmens, M. Grove, M. Fischer, G. Güntherodt, Valeri N. Kotov, H. Kageyama, K. Onizuka, Y. Ueda
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] .  ... 
doi:10.1103/physrevlett.85.2605 pmid:10978118 fatcat:vkuap245w5batpj2olvaqjfi2u
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