# Browsing by Subject "lattice field theory"

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Item Open Access Exploring Quantum Field Theories with Qubit Lattice Models(2020) Singh, HershThe framework of quantum field theory (QFT) underlies our modern understanding of both particle physics and condensed matter physics. Despite its importance, precise quantitative calculations in strongly-coupled theories in QFTs have generally only been possible through non-perturbative lattice Monte Carlo (MC) methods. Traditionally, such lattice MC methods proceed by starting from a lattice regularization of the continuum QFT of interest, which has the same (possibly infinite dimensional) local Hilbert space at each lattice site as the continuum QFT. In this thesis, we explore an alternative regularization where the local Hilbert space is also replaced by a smaller finite dimensional Hilbert space. Motivated by the appeal of such models for near-term quantum computers, we dub this approach qubit regularization. Using this approach, in this thesis, we present three main results. First, we develop a qubit-regularization for the O(N) nonlinear sigma model (NLSM) in D $\geq$ 3 spacetime dimensions. We show using numerical lattice calculations that the O(N ) qubit model lies in the correct universality class for N = 2, 4, 6, 8, and reproduces the universal physics of the O(N) Wilson-Fisher (WF) fixed point in D = 3 spacetime dimensions by computing some well-known critical exponents. Next, we explore sectors of large global charges of the O(N) WF conformal field theory (CFT) using the O(N) qubit model. This allows us to test the predictions of a recently proposed large-charge effective field theory (EFT) and extract the two leading low-energy constants (LECs) in the EFT. Performing computations for N = 2, 4, 6, 8, we are also able to quantitatively test predictions of a recent large-N analysis in the large-charge sectors. Finally, we show that our qubit approach can also be used to study the few-body physics of non-relativistic particles. In particular, we consider a system of two species of mass-imbalanced fermions in $1 + 1$ dimensions. We compute the ground state energies for a range of mass-imbalances and interaction strengths, and uncover some problems with recent results obtained from the Complex Langevin (CL) method for the same system.

Item Open Access Fermion Bag Approach for Hamiltonian Lattice Field Theories(2018) Huffman, EmilieUnderstanding the critical behavior near quantum critical points for strongly correlated quantum many-body systems remains intractable for the vast majority of scenarios. Challenges involve determining if a quantum phase transition is first- or second-order, and finding the critical exponents for second-order phase transitions. Learning about where second-order phase transitions occur and determining their critical exponents is particularly interesting, because each new second-order phase transition defines a new quantum field theory.

Quantum Monte Carlo (QMC) methods are one class of techniques that, when applicable, offer reliable ways to extract the nonperturbative physics near strongly coupled quantum critical points. However, there are two formidable bottlenecks to the applicability of QMC: (1) the sign problem and (2) algorithmic update inefficiencies. In this thesis, I overcome both these difficulties for a class of problems by extending the fermion bag approach recently developed by Shailesh Chandrasekharan to the Hamiltonian formalism and by demonstrating progress using the example of a specific quantum system known as the $t$-$V$ model, which exhibits a transition from a semimetal to an insulator phase for a single flavor of four-component Dirac fermions.

I adapt the fermion bag approach, which was originally developed in the context of Lagrangian lattice field theories, to be applicable within the Hamiltonian formalism, and demonstrate its success in two ways: first, through solutions to new sign problems, and second, through the development of new efficient QMC algorithms. In addressing the first point, I present a solution to the sign problem for the $t$-$V$ model. While the $t$-$V$ model is the simplest Gross-Neveu model of the chiral Ising universality class, the specter of the sign problem previously prevented its simulation with QMC for 30 years, and my solution initiated the first QMC studies for this model. The solution is then extended to many other Hamiltonian models within a class that involves fermions interacting with quantum spins. Some of these models contain an interesting quantum phase transition between a massless/semimetal phase to a massive/insulator phase in the so called Gross-Neveu universality class. Thus, the new solutions to the sign problem allow for the use of the QMC method to study these universality classes.

The second point is addressed through the construction of a Hamiltonian fermion bag algorithm. The algorithm is then used to compute the critical exponents for the second-order phase transition in the $t$-$V$ model. By pushing the calculations to significantly larger lattice sizes than previous recent computations ($64^2$ sites versus $24^2$ sites), I am able to compute the critical exponents more reliably here compared to earlier work. I show that the inclusion of these larger lattices causes a significant shift in the values of the critical exponents that was not evident for the smaller lattices. This shift puts the critical exponent values in closer agreement with continuum $4-\epsilon$ expansion calculations. The largest lattice sizes of $64^2$ at a comparably low temperature are reachable due to efficiency gains from this Hamiltonian fermion bag algorithm. The two independent critical exponents I find, which completely characterize the phase transition, are $\eta=.51(3)$ and $\nu=.89(1)$, compared to previous work that had lower values for these exponents. The finite size scaling fit is excellent with a $\chi^2/DOF=.90$, showing strong evidence for a second-order critical phase transition, and hence a non-perturbative QFT can be defined at the critical point.