A Finite-Temperature Generalisation of the Coupled Cluster Method: A Non-Perturbative Access to Grand Partition Functions

We present an ab initio auxiliary field quantum Monte Carlo method for studying the electronic structure of molecules, solids, and model Hamiltonians at finite temperature. The algorithm marries the ab initio phaseless auxiliary field quantum Monte Carlo algorithm known to produce high accuracy ground state energies of molecules and solids with its finite temperature variant, long used by condensed matter physicists for studying model Hamiltonian phase diagrams, to yield a phaseless, ab initio finite temperature method. We demonstrate that the method produces internal energies within chemical accuracy of exact diagonalization results across a wide range of temperatures for HO (STO-3G), C (STO-6G), the one-dimensional hydrogen chain (STO-6G), and the multiorbital Hubbard model. Our method effectively controls the phase problem through importance sampling, often even without invoking the phaseless approximation, down to temperatures at which the systems studied approach their ground states and may therefore be viewed as exact over wide temperature ranges. This technique embodies a versatile tool for studying the finite temperature phase diagrams of a plethora of systems whose properties cannot be captured by a Hubbard U term alone. Our results moreover illustrate that the severity of the phase problem for model Hamiltonians far exceeds that for many molecules at all of the temperatures studied.

Section: Introductionmentioning

confidence: 99%

Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo

Liu

Cho

Rubenstein

2018

“…However, their formalism requires knowledge of the spectrum of the interacting Hamiltonian and is therefore ill-suited to computations on realistic systems. Mukherjee and coworkers have developed a more practical method which they have termed the thermal cluster cumulant (TCC) method [44][45][46][47][48] . This method is based on a thermally normal ordered exponential ansatz for the interaction picture imaginary-time propagator.…”

Section: Introductionmentioning

confidence: 99%

A Time-Dependent Formulation of Coupled-Cluster Theory for Many-Fermion Systems at Finite Temperature

White

Chan

2018

We present a time-dependent formulation of coupled cluster theory. This theory allows for direct computation of the free energy of quantum systems at finite temperature by imaginary time integration and is closely related to the thermal cluster cumulant theory of Mukherjee and co-workers. Our derivation highlights the connection to perturbation theory and zero-temperature coupled cluster theory. We show explicitly how the finite-temperature coupled cluster singles and doubles amplitude equations can be derived in analogy with the zero-temperature theory and how response properties can be efficiently computed using a variational Lagrangian. We discuss the implementation for realistic systems and showcase the potential utility of the method with calculations of the exchange correlation energy of the uniform electron gas at warm dense matter conditions. arXiv:1807.09961v2 [physics.chem-ph]

“…Here, we present a method to model finite-temperature electronic dynamics that is suited to ab initio simulations of condensed phase systems as well as molecules. We work within the coupled cluster framework, which has enjoyed great popularity for solving the zero-temperature electronic structure problem, [39][40][41][42] and where extensions to periodic solids [43][44][45][46] , finite temperatures [47][48][49][50] , and open systems 51 have become areas of recent research. From a theoretical perspective, one can either start from the equation-of-motion for the density matrix or from a thermofield formalism which propagates a pure state in an extended Hilbert space [52][53][54] .…”

Section: Introductionmentioning

confidence: 99%

Time-Dependent Coupled Cluster Theory on the Keldysh Contour for Nonequilibrium Systems

White

Chan

2019

We leverage the Keldysh formalism to extend our implementation of finite temperature coupled cluster theory [J. Chem. Theory Comput. 2018, 14, 5690-5700] to thermal systems that have been driven out of equilibrium. The resulting Keldysh coupled cluster theory is discussed in detail. We describe the implementation of the equations necessary to perform Keldysh coupled cluster singles and doubles calculations of finite temperature dynamics, and we apply the method to some simple systems including a Hubbard model with a Peierls phase and an ab initio model of warm-dense silicon subject to an ultrafact XUV pulse. II. THEORY