Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Exact excited states of nonintegrable models

Journal Article · · Physical Review. B
 [1];  [2];  [3];  [4]
  1. Princeton Univ., NJ (United States); DOE/OSTI
  2. Univ. of Melbourne, Parkville, VIC (Australia); Technische Univ. Dresden (Germany); Princeton Univ., NJ (United States)
  3. Princeton Univ., NJ (United States); Donostia International Physics Center (Spain); Univ. Paris Diderot-Sorbonne Paris Cité, Paris Cedex (France); Sorbonne Univ., Paris (France)
  4. Univ. Paris Diderot-Sorbonne Paris Cité, Paris Cedex (France); Princeton Univ., NJ (United States)
+ Show Author Affiliations
We discuss a method of numerically identifying exact energy eigenstates for a finite system, whose form can then be obtained analytically. We demonstrate our method by identifying and deriving exact analytic expressions for several excited states, including an infinite tower, of the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) model, a celebrated nonintegrable model. The states thus obtained for the AKLT model can be interpreted as from one to an extensive number of quasiparticles on the ground state or on the highest excited state when written in terms of dimers. Included in these exact states is a tower of states spanning energies from the ground state to the highest excited state. Here, some of the states of the tower appear to be in the bulk of the energy spectrum, allowing us to make conjectures on the strong eigenstate thermalization hypothesis. We also generalize these exact states including the tower of states to the generalized integer spin AKLT models. Furthermore, we establish a correspondence between some of our states and those of the Majumdar-Ghosh model, yet another nonintegrable model, and extend our construction to the generalized integer spin AKLT models.
Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
SC0016239
OSTI ID:
1612429
Alternate ID(s):
OSTI ID: 1488983
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 23 Vol. 98; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (96)

Rigorous Results on Valence-Bond Ground States in Antiferromagnets book January 2004
A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state journal October 1988
Entanglement and Density Matrix of a Block of Spins in AKLT Model journal September 2008
On Many-Body Localization for Quantum Spin Chains journal April 2016
Some exact excited states in a linear antiferromagnetic spin system journal February 1982
Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model journal February 1983
Two exact excited states for the S = 1 AKLT chain journal May 1989
Universality of the correlations between eigenvalues of large random matrices journal August 1993
Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states journal May 2006
The density-matrix renormalization group in the age of matrix product states journal January 2011
A practical introduction to tensor networks: Matrix product states and projected entangled pair states journal October 2014
One-dimensional quasi-exactly solvable Schrödinger equations journal June 2016
Thermalization and its mechanism for generic isolated quantum systems journal April 2008
Localization and topology protected quantum coherence at the edge of hot matter journal July 2015
Weak ergodicity breaking from quantum many-body scars journal May 2018
On Next‐Nearest‐Neighbor Interaction in Linear Chain. I journal August 1969
The Majumdar-Ghosh chain. Twofold ground state and elementary excitations journal September 1984
Transfer matrices and excitations with matrix product states journal May 2015
Area laws in a many-body localized state and its implications for topological order journal September 2013
Failure of the generalized eigenstate thermalization hypothesis in integrable models with multiple particle species journal September 2014
Entanglement analysis of isotropic spin-1 chains journal July 2015
Three magnons in an isotropic S   =  1 ferromagnetic chain as an exactly solvable non-integrable system journal March 2016
Long coherence times for edge spins journal June 2017
Bethe ansatz for two-magnon scattering states in 2D and 3D Heisenberg–Ising ferromagnets journal April 2018
Entanglement of disjoint blocks in the one-dimensional spin-1 VBS journal March 2012
Quantum statistical mechanics in a closed system journal February 1991
Negativity for two blocks in the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki model journal December 2011
S =2 antiferromagnetic quantum spin chain journal August 1996
Matrix product states represent ground states faithfully journal March 2006
Exact results for SU(3) spin chains: Trimer states, valence bond solids, and their parent Hamiltonians journal February 2007
Localization of interacting fermions at high temperature journal April 2007
Valence bond solids for SU ( n ) spin chains: Exact models, spinon confinement, and the Haldane gap journal May 2007
Exact analysis of entanglement in gapped quantum spin chains journal July 2007
Spinon confinement and the Haldane gap in SU ( n ) spin chains journal November 2009
Entanglement spectrum of a topological phase in one dimension journal February 2010
Topological quantum phase transition in an S = 2 spin chain journal June 2010
Many-body localization phase transition journal November 2010
Critical theory of the topological quantum phase transition in an S = 2 spin chain journal December 2010
Classification of gapped symmetric phases in one-dimensional spin systems journal January 2011
Quantum quenches, thermalization, and many-body localization journal March 2011
Symmetry protection of topological phases in one-dimensional quantum spin systems journal February 2012
Localization-protected quantum order journal July 2013
Many-body localization and symmetry-protected topological order journal April 2014
Many-body localization edge in the random-field Heisenberg chain journal February 2015
Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries journal June 2018
Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations journal October 2018
Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis journal December 2018
Chaos and quantum thermalization journal August 1994
Eigenstate thermalization within isolated spin-chain systems journal January 2013
Finite-size scaling analysis of the eigenstate thermalization hypothesis in a one-dimensional interacting Bose gas journal January 2013
Finite-size scaling of eigenstate thermalization journal April 2014
Testing whether all eigenstates obey the eigenstate thermalization hypothesis journal November 2014
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States journal July 2008
Breakdown of Thermalization in Finite One-Dimensional Systems journal September 2009
Absence of Thermalization in Nonintegrable Systems journal January 2011
Many-Body Localization in One Dimension as a Dynamical Renormalization Group Fixed Point journal February 2013
Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles journal February 2013
Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis journal July 2017
Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State journal April 1983
Rigorous results on valence-bond ground states in antiferromagnets journal August 1987
Extended Heisenberg models of antiferromagnetism: Analogies to the fractional quantum Hall effect journal February 1988
Entanglement in a Valence-Bond Solid State journal November 2004
Prethermal Strong Zero Modes and Topological Qubits journal December 2017
Does a Single Eigenstate Encode the Full Hamiltonian? journal April 2018
Relaxation and Prethermalization in an Isolated Quantum System journal September 2012
Entanglement in Valence-Bond-Solid States journal April 2010
Bethe-Ansatz Approximation for the S =1 Antiferromagnetic Spin Chain journal October 1994
Many-Body Localization and Thermalization in Quantum Statistical Mechanics journal March 2015
Ergodicity breaking in a model showing many-body localization journal February 2013
Poisson vs. GOE Statistics in Integrable and Non-Integrable Quantum Hamiltonians journal June 1993
Spin 3/2 dimer model journal May 2009
Entanglement and Density Matrix of a Block of Spins in AKLT Model text January 2008
Breakdown of thermalization in finite one-dimensional systems text January 2009
Entanglement in Valence-Bond-Solid States text January 2009
Symmetry protection of topological order in one-dimensional quantum spin systems text January 2009
Topological quantum phase transition in an S=2 spin chain text January 2010
The density-matrix renormalization group in the age of matrix product states text January 2010
The many-body localization phase transition text January 2010
Many-body localization in one dimension as a dynamical renormalization group fixed point text January 2012
Ergodicity breaking in a model showing many-body localization text January 2012
Area laws in a many-body localized state and its implications for topological order text January 2013
Localization and topology protected quantum coherence at the edge of 'hot' matter preprint January 2013
Finite-size scaling of eigenstate thermalization text January 2013
Many body localization and thermalization in quantum statistical mechanics text January 2014
Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species text January 2014
Many-body localization edge in the random-field Heisenberg chain text January 2014
Entanglement analysis of isotropic spin-1 chains text January 2015
Does a single eigenstate encode the full Hamiltonian? text January 2015
Three magnons in an isotropic $S=1$ ferromagnetic chain as an exactly solvable non-integrable system text January 2015
Bethe Ansatz for two-magnon scattering states in 2D and 3D Heisenberg-Ising ferromagnets text January 2017
Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations text January 2018
Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states text January 2005
Localization of interacting fermions at high temperature text January 2006
Exact Analysis of Entanglement in Gapped Quantum Spin Chains text January 2007
Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap text January 2007
Chaos and Quantum Thermalization text January 1994

Cited By (31)

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations journal October 2018
Proof of the absence of local conserved quantities in the XYZ chain with a magnetic field journal November 2019
Reply to "Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"" by Mondaini et.al text January 2017
Weak ergodicity breaking from quantum many-body scars journal May 2018
Connection between quantum-many-body scars and the Affleck–Kennedy–Lieb–Tasaki model from the viewpoint of embedded Hamiltonians journal August 2019
Nonthermal States Arising from Confinement in One and Two Dimensions journal April 2019
Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain journal April 2019
Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models journal July 2019
Exact Localized and Ballistic Eigenstates in Disordered Chaotic Spin Ladders and the Fermi-Hubbard Model journal July 2019
Low-energy dynamics of the Affleck-Kennedy-Lieb-Tasaki model in the one- and two-triplon basis journal October 2019
Quantum many-body scars from magnon condensation journal November 2019
Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization journal December 2019
Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals journal January 2020
Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis journal December 2018
Operator spreading in quantum maps journal March 2019
Signatures of rare states and thermalization in a theory with confinement journal May 2019
Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars journal June 2019
Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 X Y Magnets journal October 2019
Entanglement-Ergodic Quantum Systems Equilibrate Exponentially Well journal November 2019
Topological many-body scar states in dimensions one, two, and three journal December 2019
Fractons from confinement in one dimension journal January 2020
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians journal February 2020
Slow Quantum Thermalization and Many-Body Revivals from Mixed Phase Space journal March 2020
Entanglement-ergodic quantum systems equilibrate exponentially well text January 2019
Operator Spreading in Quantum Maps text January 2018
Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain text January 2018
Emergent SU(2) dynamics and perfect quantum many-body scars text January 2018
Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians text January 2019
Slow quantum thermalization and many-body revivals from mixed phase space text January 2019
Low-energy dynamics of the Affleck-Kennedy-Lieb-Tasaki model in the one- and two-triplon basis text January 2019
Topological many-body scar states in dimensions one, two, and three text January 2019

Similar Records

Large classes of quantum scarred Hamiltonians from matrix product states
Journal Article · Mon Aug 10 20:00:00 EDT 2020 · Physical Review. B · OSTI ID:1802874
η-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars
Journal Article · Wed Aug 19 20:00:00 EDT 2020 · Physical Review. B · OSTI ID:1802875
Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis
Journal Article · Wed Dec 26 19:00:00 EST 2018 · Physical Review. B · OSTI ID:1612430

Related Subjects

1-dimensional spin chains
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Exact solutions for many-body systems
Materials Science
Physics
Spin lattice models