Variational wavefunctions for Sachdev-Ye-Kitaev models

Abstract

Given a class of $q$-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground state energy in the thermodynamic limit? Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, like for the Sachdev-Ye-Kitaev (SYK) models. This prompts us to propose a new class of wavefunctions for SYK models inspired by the variational coupled cluster algorithm. We introduce a static ("0+0D") large-$N$ field theory to study the energy, two-point correlators, and entanglement properties of these states. Most importantly, we demonstrate a finite disorder-averaged approximation ratio of $r\approx 0.62$ between the variational and ground state energy of SYK for $q=4$. Moreover, the variational states provide an exact description of spontaneous symmetry breaking in a related two-flavor SYK model.

arXiv comment6 pages

References in corpus (46)

• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Scalable Quantum Simulation of Molecular Energies
• Quantum entanglement in condensed matter systems
• Hartree-Fock on a superconducting qubit quantum computer
• Traversable Wormholes via a Double Trace Deformation
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Bekenstein-Hawking Entropy and Strange Metals
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Holographic metals and the fractionalized Fermi liquid
• A Universal Operator Growth Hypothesis
• Diving into traversable wormholes
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• A strongly correlated metal built from Sachdev-Ye-Kitaev models
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• Eternal traversable wormhole
• Numerical study of fermion and boson models with infinite-range random interactions
• Quantum quench of the Sachdev-Ye-Kitaev Model
• Quantum Hamiltonian Complexity
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
• Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Magnetotransport in a model of a disordered strange metal
• Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK
• Quantum Entanglement of the Sachdev-Ye-Kitaev Models
• Transition from overscreening to underscreening in the multichannel Kondo model: exact solution at large N
• Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals
• Pure states in the SYK model and nearly-$Ad{S}_2$ gravity
• Eigenstate entanglement in the Sachdev-Ye-Kitaev model
• Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions
• Local Hamiltonians Whose Ground States are Hard to Approximate
• Chaos in a classical limit of the Sachdev-Ye-Kitaev model
• Quench, thermalization and residual entropy across a non-Fermi liquid to Fermi liquid transition
• Low-rank Sachdev-Ye-Kitaev models
• A Sparse Model of Quantum Holography
• Universal Constraints on Energy Flow and SYK Thermalization
• Approximation algorithms for quantum many-body problems
• The Coupled SYK model at Finite Temperature
• Entanglement Entropy and its Quench Dynamics for Pure States of the Sachdev-Ye-Kitaev model
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Approximation algorithms for QMA-complete problems
• Strange Half Metals and Mott Insulators in SYK Models
• Cluster expansion for ground states of local Hamiltonians
• Approximating random quantum optimization problems

Cited by in corpus (12)

• Surprises in the Deep Hilbert Space of all-to-all systems: From super-exponential scrambling to slow entanglement growth
• Optimizing sparse fermionic Hamiltonians
• Can neural quantum states learn volume-law ground states?
• Non-Stabilizerness of Sachdev-Ye-Kitaev Model
• Neural-Shadow Quantum State Tomography
• NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians
• Bounds on the ground state energy of quantum $p$-spin Hamiltonians
• Nematic phases and elastoresistivity from a multiorbital non-Fermi liquid
• Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model
• Efficiency of the hidden fermion determinant states Ansatz in the light of different complexity measures
• A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics
• Optimizing Sparse SYK