Method to identify parent Hamiltonians for trial states

We describe a general method to identify exact, local parent Hamiltonians for trial states like quantum Hall or spin liquid states, which we have used extensively during the past decade. It can be used to identify exact parent Hamiltonians, either directly or via the construction of simpler annihilation operators from which a parent Hamiltonian respecting all the required symmetries can be constructed. Most remarkably, however, the method provides approximate parent Hamiltonians whenever an exact solution is not available within the space of presumed interaction terms.

[1]  E. Witten.  Non-abelian bosonization in two dimensions , 1984 .

[2]  Gregory W. Moore,et al.  Nonabelions in the fractional quantum Hall effect , 1991 .

[3]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[4]  Shastry,et al.  Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions. , 1988, Physical review letters.

[5]  Haldane,et al.  Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-(1/2 antiferromagnetic Heisenberg chain with 1/r2 exchange. , 1988, Physical review letters.

[6]  Zou,et al.  Properties of the chiral-spin-liquid state. , 1990, Physical review. B, Condensed matter.

[7]  Kawakami.  SU(N) generalization of the Gutzwiller-Jastrow wave function and its critical properties in one dimension. , 1992, Physical review. B, Condensed matter.

[8]  R. Richardson.  A restricted class of exact eigenstates of the pairing-force Hamiltonian , 1963 .

[9]  M. Greiter.  Mapping of Parent Hamiltonians , 2011 .

[10]  R. Laughlin.  Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations , 1983 .

[11]  F. Wilczek,et al.  Paired Hall states , 1992 .

[12]  R. Laughlin,et al.  Equivalence of the resonating-valence-bond and fractional quantum Hall states. , 1987, Physical review letters.

[13]  R. Richardson.  Pairing in the limit of a large number of particles , 1977 .

[14]  Ching Hua Lee,et al.  Geometric construction of Quantum Hall clustering Hamiltonians , 2015, 1502.04663.

[15]  M. Gutzwiller.  Effect of Correlation on the Ferromagnetism of Transition Metals , 1963 .

[16]  Vollhardt,et al.  Correlation functions for Hubbard-type models: The exact results for the Gutzwiller wave function in one dimension. , 1987, Physical review letters.

[17]  F. Haldane,et al.  Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States , 1983 .

[18]  Bryan K. Clark,et al.  Computational Inverse Method for Constructing Spaces of Quantum Models from Wave Functions , 2018, Physical Review X.

[19]  M. Greiter.  Microscopic formulation of the hierarchy of quantized Hall states , 1993, cond-mat/9311062.

[20]  N. Read,et al.  Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level , 1998, cond-mat/9809384.

[21]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[22]  G. Sierra,et al.  Quantum spin Hamiltonians for the SU(2)k WZW model , 2011, 1109.5470.

[23]  R. Thomale,et al.  Spin hamiltonian for which the chiral spin liquid is the exact ground state. , 2007, Physical review letters.

[24]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[25]  R. Thomale,et al.  Non-Abelian statistics in a quantum antiferromagnet. , 2009, Physical Review Letters.

[26]  Bernard,et al.  Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory. , 1992, Physical review letters.

[27]  R. Thomale,et al.  Parent Hamiltonian for the non-Abelian chiral spin liquid , 2012, 1201.5312.

[28]  Ady Stern,et al.  Anyons and the quantum Hall effect - a pedagogical review , 2007, 0711.4697.

[29]  Pierre Mathieu,et al.  Conformal Field Theory , 1999 .

[30]  Vollhardt,et al.  Ground-state properties of correlated fermions: Exact analytic results for the Gutzwiller wave function. , 1987, Physical review letters.

[31]  Frank Wilczek,et al.  Fractional Statistics and the Quantum Hall Effect , 1984 .

[32]  Haldane,et al.  Critical theory of quantum spin chains. , 1987, Physical review. B, Condensed matter.

[33]  Yokoyama,et al.  Exactly soluble supersymmetric t-J-type model with long-range exchange and transfer. , 1991, Physical review letters.