We consider a restricted Boltzmann Machine (RBM) correlated BCS wave function as the ground state of the two-dimensional Hubbard model and study its electronic and magnetic properties as a function of hole doping. We compare the results with those obtained by using conventional Jastrow projectors. The results show that the RBM wave function outperforms the Jastrow projected ones in the underdoped region inmterms of the variational energy. Computation of superconducting (SC) correlations in the model shows that the RBM wave function gives slightly weaker SC correlations as compared to the Jastrow projected wave functions. A significant advantage of the RBM wave function is that it spontaneously gives rise to strong antiferromagnetic (AF) correlations in the underdoped region even though the wave function does not incorporate any explicit AF order. In comparison, AF correlations in the Jastrow projected wave functions are found to be very weak. These and other results obtained show that the RBM wave function provides an improved description of the phase diagram of the model. The work also demonstrates the power of neural-network quantum state (NQS) wave functions in the study of strongly correlated electron systems.We consider a restricted Boltzmann Machine (RBM) correlated BCS wave function as the ground state of the two-dimensional Hubbard model and study its electronic and magnetic properties as a function of hole doping. We compare the results with those obtained by using conventional Jastrow projectors. The results show that the RBM wave function outperforms the Jastrow projected ones in the underdoped region inmterms of the variational energy. Computation of superconducting (SC) correlations in the model shows that the RBM wave function gives slightly weaker SC correlations as compared to the Jastrow projected wave functions. A significant advantage of the RBM wave function is that it spontaneously gives rise to strong antiferromagnetic (AF) correlations in the underdoped region even though the wave function does not incorporate any explicit AF order. In comparison, AF correlations in the Jastrow projected wave functions are found to be very weak. These and other results obtained show that the RBM wave function provides an improved description of the phase diagram of the model. The work also demonstrates the power of neural-network quantum state (NQS) wave functions in the study of strongly correlated electron systems.

arXiv:2412.04103Dec 5, 20240 citations

Correlated Ground-State Wavefunctions

WORLD SCIENTIFIC eBooksOct 1, 20120 citations

d-Wave State with Multiplicative Correlation Factors for the Hubbard Model

Takashi Yanagisawa, Soh Koike, Yamaji K.

A d -wave state wave function with multiplicative correlation factors for the Hubbard model is investigated using a variational Monte Carlo method. Employing a simple Gutzwiller-BCS wave function as a starting wave function, we consider improved wave functions with off-diagonal correlation factors. The Monte Carlo simulations are carried out on a square lattice with size 10×10 for U =8 and next nearest neighbor transfer t '=-0.09. The ground-state energy is evaluated from an extrapolation. Our wave functions show that pair correlation functions are enhanced for a negative value of t '.A d -wave state wave function with multiplicative correlation factors for the Hubbard model is investigated using a variational Monte Carlo method. Employing a simple Gutzwiller-BCS wave function as a starting wave function, we consider improved wave functions with off-diagonal correlation factors. The Monte Carlo simulations are carried out on a square lattice with size 10×10 for U =8 and next nearest neighbor transfer t '=-0.09. The ground-state energy is evaluated from an extrapolation. Our wave functions show that pair correlation functions are enhanced for a negative value of t '.

Journal of the Physical Society of JapanNov 15, 199930 citations

Correlation functions of solvable models

Bernard Nienhuis

Elsevier eBooksJan 1, 19941 citation

Resonating valence-bond physics on the honeycomb lattice

Pranay Patil, Ishita Dasgupta, Kedar Damle

We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric $S=1/2$ antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{w}(2)}$, where $\mathbf{Q}=(2\ensuremath{\pi}/3,\ensuremath{-}2\ensuremath{\pi}/3)$ is the wave vector corresponding to ``columnar'' valence-bond solid order on the honeycomb lattice, and ${\ensuremath{\eta}}_{w}(2)\ensuremath{\approx}1.49(3)$. We use a recently introduced large- $g$ expansion approach to relate bond-energy correlators of the $\mathrm{SU}(g)$ wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength $V(g)=\ensuremath{-}ln(1+1/{g}^{2})$. Putting $g=2$ , we find numerically that the dimer correlation function ${D}^{d}(\stackrel{P\vec}{r})$ of this dimer model has power-law behavior ${D}^{d}(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{d}(2)}$ with ${\ensuremath{\eta}}_{d}(2)\ensuremath{\approx}1.520(15)$, in rather good agreement with the wave function results. We also study the same quantities for $g=3,4,10$ and find that the bond-energy correlations in the $\mathrm{SU}(g)$ wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model.We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric $S=1/2$ antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{w}(2)}$, where $\mathbf{Q}=(2\ensuremath{\pi}/3,\ensuremath{-}2\ensuremath{\pi}/3)$ is the wave vector corresponding to ``columnar'' valence-bond solid order on the honeycomb lattice, and ${\ensuremath{\eta}}_{w}(2)\ensuremath{\approx}1.49(3)$. We use a recently introduced large-$g$ expansion approach to relate bond-energy correlators of the $\mathrm{SU}(g)$ wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength $V(g)=\ensuremath{-}ln(1+1/{g}^{2})$. Putting $g=2$, we find numerically that the dimer correlation function ${D}^{d}(\stackrel{P\vec}{r})$ of this dimer model has power-law behavior ${D}^{d}(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{d}(2)}$ with ${\ensuremath{\eta}}_{d}(2)\ensuremath{\approx}1.520(15)$, in rather good agreement with the wave function results. We also study the same quantities for $g=3,4,10$ and find that the bond-energy correlations in the $\mathrm{SU}(g)$ wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model.

arXiv:1408.4374Physical Review BDec 15, 201412 citations

Strongly Correlated Systems

Adolfo Avella, Ferdinando Mancini

Springer series in solid-state sciencesJan 1, 201394 citations

We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric

S=1/2

antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{w}(2)}$, where $\mathbf{Q}=(2\ensuremath{\pi}/3,\ensuremath{-}2\ensuremath{\pi}/3)$ is the wave vector corresponding to ``columnar'' valence-bond solid order on the honeycomb lattice, and ${\ensuremath{\eta}}_{w}(2)\ensuremath{\approx}1.49(3)$. We use a recently introduced large-

g

expansion approach to relate bond-energy correlators of the

\mathrm{SU}(g)

wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength $V(g)=\ensuremath{-}ln(1+1/{g}^{2})$. Putting

g=2

, we find numerically that the dimer correlation function ${D}^{d}(\stackrel{P\vec}{r})$ of this dimer model has power-law behavior ${D}^{d}(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{d}(2)}$ with ${\ensuremath{\eta}}_{d}(2)\ensuremath{\approx}1.520(15)$, in rather good agreement with the wave function results. We also study the same quantities for

g=3,4,10

and find that the bond-energy correlations in the

\mathrm{SU}(g)

wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model.