Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin-densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at non-zero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H$_2$ molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. It is shown that (and in what sense) the static charge density wave is a soft plasmon.
Many-body ergodicity breaking from wavefunction snapshots
International School for Advanced Studies (SISSA)（国际高等研究学院）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜勒·萨拉姆理论物理国际中心）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）；INFN, Sezione di Bologna（意大利国家核物理研究所博洛尼部分所）；J. Stefan Institute（约热·斯特凡研究所）；University of Ljubljana（卢布尔雅那大学）；Wrocław University of Science and Technology（弗罗茨瓦夫理工大学）
We present three distinct examples where phaseless auxiliary-field Quantum Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant trial wavefunction with essential symmetry breaking. We first utilized essential time-reversal symmetry breaking with ph-AFQMC to compute the triplet-singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complex-restricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the single-triplet gap of a known biradicaloid, C$_{36}$.…
The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. The theory of quantum entanglement is currently leading to a paradigm shift in understanding quantum correlations in many body systems and in this work we show how symmetry breaking can be understood from this wavefunction centered point of view. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of thos…
The electronic structure of the nitrogenase metal cofactors is central to nitrogen fixation. However, the P-cluster and iron molybdenum cofactor, each containing eight irons, have resisted detailed characterization of their electronic properties. Through exhaustive many-electron wavefunction simulations enabled by new theoretical methods, we report on the low-energy electronic states of the P-cluster in three oxidation states. The energy scales of orbital and spin excitations overlap, yielding a dense spectrum with features we trace to the underlying atomic states and recouplings. The clusters…
We show, in several important and general cases, that a low variational energy density of a trial state is possible even when the trial state represents a different phase from the ground state. Specifically, we ask whether the ground state energy density of a Hamiltonian whose ground state is in phase A can be approximated to arbitrary accuracy by a wavefunction which represents a different phase B. We show this is indeed the case when A has discrete symmetry breaking order in one dimension or topological order in two dimensions, while B is disordered. We argue that, if reasonable conditions o…
Employing the Haldane-Rezayi periodic representation, the crystalline determinantal Hall crystal mean field solutions derived in previous works are used to construct variational wavefunctions for the FQHE at $ν=1/q$. The proposed states optimize the short range correlations in a similar measure as the Laughlin ones, since the zero of the states when the coordinates of two particles join is of order $q$. However, the proposed wavefunctions also incorporate the crystalline correlations of the mean field problem, through a determinantal mean field function entering their construction. The above p…
Wavefunctions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included \textit{a posteriori}. In this article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allow us to …
Unconventional superconductivity is characterized by the spontaneous symmetry breaking of the macroscopic superconducting wavefunction in addition to the gauge symmetry breaking, such as rotational-symmetry breaking with respect to the underlying crystal-lattice symmetry. Particularly, superconductivity with spontaneous rotational-symmetry breaking in the wavefunction amplitude and thus in bulk properties, not yet reported previously, is intriguing and can be termed "nematic" superconductivity in analogy to nematic liquid-crystal phases. Here, based on specific-heat measurements of the single-…
It has been well established that for symmetry protected topological systems, the non-trivial topology prevents a real space representation using exponentially localized Wannier wavefunctions (WFs) in all directions, unless the protecting symmetry is sacrificed as an on-site transformation. This makes it challenging to determine the symmetry of various physical observables represented using such WFs. In this work, we propose a practical method for overcoming such challenges using the Kane-Mele model as a concrete example. We present a systematic procedure for diagnosing the symmetry of any obs…
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…
We perform numerical studies to determine if the fractional quantum Hall state observed at filling nu=5/2 is the Moore-Read wavefunction or its particle hole conjugate, the so-called AntiPfaffian. Using a truncated Hilbert space approach we find that for realistic interactions, including Landau-level mixing, the ground state remains fully polarized and the AntiPfaffian is strongly favored.
Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is no local order parameter for SPT phases. Here we employ a tensor-network method to compute the topological invariants characterized by the simulated modular $S$ and $T$ matrices to study transitions in a few families of two-dimensional (2D) wavefunctions which are $\mathbb{Z}_N$ ($N=2\, \&3$) symmetric. We find that in addition to the topologically ordered ph…
We use the microscopic Hartree-Fock approximation to investigate various quantum phase transitions associated with possible spontaneous symmetry breaking induced by a tilted magnetic field in the integral quantum Hall regime of wide parabolic wells and zero width double well (bilayer) systems. We propose a general class of variational wavefunctions that describe several types of parity, spin, and translational symmetry breaking, including spin and charge density wave phases. Zero temperature quantum phase diagrams for these systems are calculated in the parameter regime of experimental interes…
Intertwining of spin, charge and pairing correlations in the repulsive two-dimensional Hubbard model is shown through unrestricted variational calculations, with projected wavefunctions free of symmetry breaking. A crossover from incommensurate antiferromagnetism to stripe order naturally emerges in the hole-doped region when increasing the on-site coupling. Although effective pairing interactions are identified, they are strongly fragmented in several modes including d-wave pairing and more exotic channels related to an underlying stripe. We demonstrate that the entanglement of a mean-field w…
We study Bose-Hubbard models on tight-binding, non-Bravais lattices, with a filling of one boson per unit cell -- and thus fractional site filling. At integer filling of a unit cell neither symmetry breaking nor topological order is required, and in principle a trivial and featureless (i.e., symmetry-unbroken) insulator is allowed. We demonstrate by explicit construction of a family of wavefunctions that such a featureless Mott insulating state exists at 1/3 filling on the kagome lattice, and construct Hamiltonians for which these wavefunctions are exact ground states. We briefly comment on th…
For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in terms of the fidelity between a ground state and its symmetry-transformed counterpart, and are computed through tensor network representations of the ground-state wavefunction. To illustrate our scheme, we consider three quantum systems on an infinite lattice in one spatial dimension, namely, the quantum Ising model in a transverse magnetic field, the quantum…
We show that the topological index of a wavefunction, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, $Z_2$ topological insulators, and Spin-$1$ AKLT and Heisenberg chai…
Projected Entangled Pair States (PEPS) provide a framework for the construction of models where a single tensor gives rise to both Hamiltonian and ground state wavefunction on the same footing. A key problem is to characterize the behavior which emerges in the system in terms of the properties of the tensor, and thus of the Hamiltonian. In this paper, we consider PEPS models with $\mathbb Z_2$ on-site symmetry and study the occurence of long-range order and spontaneous symmetry breaking. We show how long-range order is connected to a degeneracy in the spectrum of the PEPS transfer operator, an…
We study the ground state properties of the spin-1/2 frustrated ferromagnetic J1-J2 Heisenberg model on the square lattice, employing projected BCS wavefunctions with spin-triplet pairings of the spinon fields as trial wavefunctions. Based on the variational Monte Carlo analysis, we argue that, in the competing coupling regime, a certain type of the projected BCS wavefunction, dubbed the projected Z2 planar state, achieves the best optimal energy among the other competing states such as the ferromagnetic state and collinear antiferromagnetic state. Like in quantum spin liquids, the projected Z…
Massachusetts Institute of Technology（麻省理工学院）；The NSF AI Institute for Artificial Intelligence and Fundamental Interactions（美国国家科学基金会人工智能与基础交互研究所）；Harvard University（哈佛大学）；University of Michigan（密歇根大学）；University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the $U(1)$ degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion syst…
