Twisted bilayer graphene (TBG) has garnered significant interest in condensed matter physics over the past few years. Here, authors present numerical investigations of TBG implementing state-of-the-art quantum chemistry methods. Using a gauge-invariant order parameter, they show ${C}_{2z}$\ensuremath{\mathcal{T}} phase transition at charge neutrality which persists noninteger fillings near neutrality. The work is first systematic study for

At a magic relative twist angle, angle twisted bilayer graphene (MATBG) has an octet of flat bands that can host strong correlation physics when partially filled. A key theoretical discovery in MATBG is the existence ferromagnetic Slater determinants as exact ground states corresponding band interacting (FBI) Hamiltonian. The FBI Hamiltonian describes behavior electrons interact with each other high-dimensional space, and constructed from structure non-interacting Bistritzer--MacDonald model...

Abstract One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is emergence ferromagnetic Slater determinants as exact ground states for interacting Hamiltonian at chiral limit. This discovery provides an explanation correlated insulating phase which has been experimentally observed half filling. work first mathematical study models systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and trilayer with...

Single layer (SL) two-dimensional transition metal dichalcogenides (TMDs), such as MoS2, ReS2, WSe2, and MoTe2 have now become the focus of intensive fundamental applied researches due to their intriguing tunable physical properties. These materials exhibit a broad range structural phases that can be induced via elastic strain, chemical doping, electrostatic field effect. transitions in turn open close band gap SL-TMDs, leading metal-insulator transitions, lead emergence more complex quantum...

Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend on unitary transform known as gauge transformation. Over past few decades, there have been many works that focused optimizing so corresponding are maximally or reflect some symmetry underlying system. this work, we consider fully nonperiodic materials where usual not well defined and optimization impractical....

Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply reinforcement to hypothesis testing, where one designs measurements that can distinguish between multiple states {ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> }| xmlns:xlink="http://www.w3.org/1999/xlink">=</sub>...

Exponentially-localized Wannier functions are a basis of the Fermi projection Hamiltonian consisting which decay exponentially fast in space. In two and three spatial dimensions, it is well understood for periodic insulators that exponentially-localized exist if only there exists an orthonormal with finite second moment (i.e. all elements satisfy $\int |\boldsymbol{x}|^2 |w(\boldsymbol{x})|^2 \,\text{d}{\boldsymbol{x}} < \infty$). this work, we establish similar result non-periodic...

Recent experiments have shown that magic angle twisted bilayer graphene (MATBG) can exhibit correlated insulator behavior at half-filling. Seminal theoretical results towards understanding this phase in MATBG has Hartree-Fock ground states (with a positive charge gap) be exact many-body of an idealized flat band interacting (FBI) Hamiltonian. We prove the absence spin and valley degrees freedom, only FBI Hamiltonian for are two ferromagnetic Slater determinants. Incorporating we provide...

Quasiparticle poisoning errors in Majorana-based qubits are not suppressed by the underlying topological properties, which undermines usefulness of this proposed platform. This work tackles issue via quasiparticle measurement. Error-detecting Majorana stabilizer codes constructed whose stabilizers can be measured means Wannier position operators. For a logical qubit encoded one these codes, Pauli error rates exponentially code distance, result tied to exponential localization functions. The...

Quasiparticle poisoning errors in Majorana-based qubits are not suppressed by the underlying topological properties, which undermines usefulness of this proposed platform. This work tackles originating from intrinsically excited quasiparticles developing an erasure conversion scheme based on local quasiparticle detection. To model such measurements, we begin constructing position operator for Kitaev chain. A measurement probe coupling to is shown allow projective measurements Wannier basis....

In this work, we derive a discrete analog of the Wigner transform over space $(\mathbb{C}^p)^{\otimes N}$ for any prime $p$ and positive integer $N$. We show that can be constructed as inverse Fourier standard Pauli matrices $p=2$ or more generally Heisenberg-Weyl group elements $p &gt; 2$. connect our work to previous construction by Wootters showing all $p$, Wootters' corresponds taking symplectic instead transform. Finally, discuss some implications these results numerical simulation...

Discriminating between quantum states is a fundamental task in information theory. Given two ${\ensuremath{\rho}}_{+}$ and ${\ensuremath{\rho}}_{\ensuremath{-}}$, the Helstrom measurement distinguishes them with minimal probability of error. However, finding experimentally implementing can be challenging for on many qubits. Due to this difficulty, there great interest identifying local schemes which are close optimal. In first part work, we generalize previous work by Acin et al. [Phys. Rev....

Discrimination between quantum states is a fundamental task in information theory. Given two arbitrary tensor-product (TPQS) $\rho_{\pm} = \rho_{\pm}^{(1)} \otimes \cdots \rho_{\pm}^{(N)}$, determining the joint $N$-system measurement to optimally distinguish hard problem. Thus, there great interest identifying local schemes that are optimal or close-to-optimal. In this work, we focus on distinguishing general TPQS. We begin by generalizing previous work Acin et al. (Phys. Rev. A 71, 032338)...

Discriminating between quantum states is a fundamental task in information theory. Given two states, ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sub> and xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> , the Helstrom measurement distinguishes them with minimal probability of error. However, finding experimentally implementing can be challenging for on many qubits. Due to this difficulty, there great interest identifying local schemes...

For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number equal to $0$) if and only Fermi projector admits an orthogonal basis with finite second moment all elements satisfy $\int |\boldsymbol{x}|^2 |w(\boldsymbol{x})|^2 \,\textrm{d}{\boldsymbol{x}} < \infty$). In this paper, we extend one direction of result non-periodic systems. particular, show existence slightly more decay ($\int |\boldsymbol{x}|^{2+\epsilon}...

One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is emergence ferromagnetic Slater determinants as exact ground states for interacting Hamiltonian at chiral limit. This discovery provides an explanation correlated insulating phase which has been experimentally observed half filling. work first mathematical study models systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and trilayer (TTG) with equal...

Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply RLNN to hypothesis testing and determine the optimal measurement strategy distinguishing between multiple states <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo fence="false" stretchy="false">{</mml:mo><mml:msub><mml:mi>&amp;#x03C1;</mml:mi><mml:mrow...

The nature of correlated states in twisted bilayer graphene (TBG) at the magic angle has received intense attention recent years. We present a numerical study an interacting Bistritzer-MacDonald (IBM) model TBG using suite methods quantum chemistry, including Hartree-Fock, coupled cluster singles, doubles (CCSD), and perturbative triples (CCSD(T)), as well chemistry formulation density matrix renormalization group method (DMRG). Our treatment is agnostic to gauge choices, hence we new...