Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions

Chertkov, Eli; Clark, Bryan K.

doi:10.1103/PhysRevX.8.031029

Title: Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions

Authors:: Chertkov, Eli; Clark, Bryan K.

Publication Date:: Fri Jul 27 00:00:00 EDT 2018

Sponsoring Org.:: USDOE

OSTI Identifier:: 1461930

Grant/Contract Number:: FG02-12ER46875

Resource Type:: Published Article

Journal Name:: Physical Review X

Additional Journal Information:: Journal Name: Physical Review X Journal Volume: 8 Journal Issue: 3; Journal ID: ISSN 2160-3308

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Citation Formats


                    Chertkov, Eli, and Clark, Bryan K. Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevX.8.031029.

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                    Chertkov, Eli, & Clark, Bryan K. Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions.  United States.  https://doi.org/10.1103/PhysRevX.8.031029

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                    Chertkov, Eli, and Clark, Bryan K. Fri .  
"Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions".  United States.  https://doi.org/10.1103/PhysRevX.8.031029.

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@article{osti_1461930,

  title        = {Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions},

  author       = {Chertkov, Eli and Clark, Bryan K.},

  abstractNote = {},

  doi          = {10.1103/PhysRevX.8.031029},

  journal      = {Physical Review X},

  number       = 3,

  volume       = 8,

  place        = {United States},

  year         = {Fri Jul 27 00:00:00 EDT 2018},

  month        = {Fri Jul 27 00:00:00 EDT 2018}

}

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Works referenced in this record:

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Title: Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions

Citation Formats

Quantum spin models with exact dimer ground states journal, June 2002

Wave functions for fractional Chern insulators journal, March 2012

Parent Hamiltonian for the non-Abelian chiral spin liquid journal, April 2014

Inverse design of disordered stealthy hyperuniform spin chains journal, February 2016

Deep learning journal, May 2015

Algorithmic design of self-assembling structures journal, June 2009

Optimizing Topographical Templates for Directed Self-Assembly of Block Copolymers via Inverse Design Simulations journal, December 2013

Parent Hamiltonian for the chiral spin liquid journal, September 2009

Does a Single Eigenstate Encode the Full Hamiltonian? journal, April 2018

Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States journal, August 1983

Probing the limitations of isotropic pair potentials to produce ground-state structural extremes via inverse statistical mechanics journal, October 2013

Quantum orders and symmetric spin liquids journal, April 2002

Inverse optimization techniques for targeted self-assembly journal, January 2009

Negative Poisson’s Ratio Materials via Isotropic Interactions journal, August 2008

Inverse methods for material design journal, May 2014

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model journal, February 2001

Optimized monotonic convex pair potentials stabilize low-coordinated crystals journal, January 2011

Designer spin systems via inverse statistical mechanics. II. Ground-state enumeration and classification journal, November 2013

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions journal, August 2015

Z 2 spin liquids in the S = 1 2 Heisenberg model on the kagome lattice: A projective symmetry-group study of Schwinger fermion mean-field states journal, June 2011

Projected wave function study of Z 2 spin liquids on the kagome lattice for the spin- 1 2 quantum Heisenberg antiferromagnet journal, July 2011

Number-conserving interacting fermion models with exact topological superconducting ground states journal, September 2017

Density matrix formulation for quantum renormalization groups journal, November 1992

Spin-liquid states on the triangular and Kagomé lattices: A projective-symmetry-group analysis of Schwinger boson states journal, November 2006

Designer spin systems via inverse statistical mechanics journal, October 2013

Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State journal, August 2007

The Resonating Valence Bond State in La2CuO4 and Superconductivity journal, March 1987

Energy Landscapes of Atomic Clusters as Black Box Optimization Benchmarks journal, December 2012

Ground-state uniqueness of the twelve-site RVB spin-liquid parent Hamiltonian on the kagome lattice journal, January 2014

Evolutionary approach for determining first-principles hamiltonians journal, April 2005

Superconductivity in correlated wavefunctions journal, June 1988

Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations journal, May 1983

Measurement-based quantum computation on cluster states journal, August 2003

Exploring one-particle orbitals in large many-body localized systems journal, March 2018

Physics of projected wavefunctions journal, January 1989

Linear independence of nearest-neighbor valence-bond states on the kagome lattice and construction of S U ( 2 ) -invariant spin- 1 2 Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state journal, October 2009

Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory journal, September 2002

Equivalence between XY and dimerized models journal, June 2010

Macroscopically Degenerate Exactly Solvable Point in the Spin- 1 / 2 Kagome Quantum Antiferromagnet journal, March 2018

From Real Materials to Model Hamiltonians With Density Matrix Downfolding journal, May 2018

The inverse band-structure problem of finding an atomic configuration with given electronic properties journal, November 1999

Projected Wave Functions and High Temperature Superconductivity journal, November 2001

Exact Parent Hamiltonian for the Quantum Hall States in a Lattice journal, November 2010

Fixed Points of Wegner-Wilson Flows and Many-Body Localization journal, August 2017

Using genetic algorithms to map first-principles results to model Hamiltonians: Application to the generalized Ising model for alloys journal, October 2005

The fractional quantum Hall effect journal, March 1999

On Next‐Nearest‐Neighbor Interaction in Linear Chain. I journal, August 1969

The spectral gap for some spin chains with discrete symmetry breaking journal, February 1996

Finding a Sparse Vector in a Subspace: Linear Sparsity Using Alternating Directions journal, October 2016

Reconstructing Quantum States from Local Data journal, December 2014

Superconductivity and the Quantum Hard-Core Dimer Gas journal, November 1988

Resonating valence bonds: A new kind of insulator? journal, February 1973

Characterizing the parent Hamiltonians for a complete set of orthogonal wave functions: An inverse quantum problem journal, June 2016

Exact results for the fractional quantum Hall effect with general interactions journal, April 1985

Negative Thermal Expansion in Single-Component Systems with Isotropic Interactions † journal, December 2007

Multiparty entanglement in graph states journal, June 2004

Antiferromagnetic model with known ground state journal, April 1970

Resonating valence bond states in the PEPS formalism journal, September 2012

Quantum spin models with exact dimer ground states
journal, June 2002

Wave functions for fractional Chern insulators
journal, March 2012

Parent Hamiltonian for the non-Abelian chiral spin liquid
journal, April 2014

Inverse design of disordered stealthy hyperuniform spin chains
journal, February 2016

Deep learning
journal, May 2015

Algorithmic design of self-assembling structures
journal, June 2009

Optimizing Topographical Templates for Directed Self-Assembly of Block Copolymers via Inverse Design Simulations
journal, December 2013

Parent Hamiltonian for the chiral spin liquid
journal, September 2009

Does a Single Eigenstate Encode the Full Hamiltonian?
journal, April 2018

Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States
journal, August 1983

Probing the limitations of isotropic pair potentials to produce ground-state structural extremes via inverse statistical mechanics
journal, October 2013

Quantum orders and symmetric spin liquids
journal, April 2002

Inverse optimization techniques for targeted self-assembly
journal, January 2009

Negative Poisson’s Ratio Materials via Isotropic Interactions
journal, August 2008

Inverse methods for material design
journal, May 2014

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model
journal, February 2001

Optimized monotonic convex pair potentials stabilize low-coordinated crystals
journal, January 2011

Designer spin systems via inverse statistical mechanics. II. Ground-state enumeration and classification
journal, November 2013

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
journal, August 2015

$Z_{2}$ spin liquids in the $S = \frac{1}{2}$ Heisenberg model on the kagome lattice: A projective symmetry-group study of Schwinger fermion mean-field states
journal, June 2011

Projected wave function study of $Z_{2}$ spin liquids on the kagome lattice for the spin- $\frac{1}{2}$ quantum Heisenberg antiferromagnet
journal, July 2011

Number-conserving interacting fermion models with exact topological superconducting ground states
journal, September 2017

Density matrix formulation for quantum renormalization groups
journal, November 1992

Spin-liquid states on the triangular and Kagomé lattices: A projective-symmetry-group analysis of Schwinger boson states
journal, November 2006

Designer spin systems via inverse statistical mechanics
journal, October 2013

Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
journal, August 2007

The Resonating Valence Bond State in La2CuO4 and Superconductivity
journal, March 1987

Energy Landscapes of Atomic Clusters as Black Box Optimization Benchmarks
journal, December 2012

Ground-state uniqueness of the twelve-site RVB spin-liquid parent Hamiltonian on the kagome lattice
journal, January 2014

Evolutionary approach for determining first-principles hamiltonians
journal, April 2005

Superconductivity in correlated wavefunctions
journal, June 1988

Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
journal, May 1983

Measurement-based quantum computation on cluster states
journal, August 2003

Exploring one-particle orbitals in large many-body localized systems
journal, March 2018

Physics of projected wavefunctions
journal, January 1989

Linear independence of nearest-neighbor valence-bond states on the kagome lattice and construction of $S U (2)$ -invariant spin- $\frac{1}{2}$ Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state
journal, October 2009

Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory
journal, September 2002

Equivalence between $XY$ and dimerized models
journal, June 2010

Macroscopically Degenerate Exactly Solvable Point in the Spin- $1 / 2$ Kagome Quantum Antiferromagnet
journal, March 2018

From Real Materials to Model Hamiltonians With Density Matrix Downfolding
journal, May 2018

The inverse band-structure problem of finding an atomic configuration with given electronic properties
journal, November 1999

Projected Wave Functions and High Temperature Superconductivity
journal, November 2001

Exact Parent Hamiltonian for the Quantum Hall States in a Lattice
journal, November 2010

Fixed Points of Wegner-Wilson Flows and Many-Body Localization
journal, August 2017

Using genetic algorithms to map first-principles results to model Hamiltonians: Application to the generalized Ising model for alloys
journal, October 2005

The fractional quantum Hall effect
journal, March 1999

On Next‐Nearest‐Neighbor Interaction in Linear Chain. I
journal, August 1969

The spectral gap for some spin chains with discrete symmetry breaking
journal, February 1996

Finding a Sparse Vector in a Subspace: Linear Sparsity Using Alternating Directions
journal, October 2016

Reconstructing Quantum States from Local Data
journal, December 2014

Superconductivity and the Quantum Hard-Core Dimer Gas
journal, November 1988

Resonating valence bonds: A new kind of insulator?
journal, February 1973

Characterizing the parent Hamiltonians for a complete set of orthogonal wave functions: An inverse quantum problem
journal, June 2016

Exact results for the fractional quantum Hall effect with general interactions
journal, April 1985

Negative Thermal Expansion in Single-Component Systems with Isotropic Interactions ^†
journal, December 2007

Multiparty entanglement in graph states
journal, June 2004

Antiferromagnetic model with known ground state
journal, April 1970

Resonating valence bond states in the PEPS formalism
journal, September 2012