arXiv subjects

Michael P. Zaletel

Publications and source records attributed to Michael P. Zaletel.

At least 73 records · Page 4Linked to original sources

arXiv2022

Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study

When the two layers of a twisted moiré system are subject to different degrees of strain, the effect is amplified by the inverse twist angle, e.g., by a factor of 50 in magic angle twisted bilayer graphene (TBG). Samples of TBG typically have heterostrains of 0.1-0.7%, increasing the bandwidth of the "flat'' bands by as much as tenfold, placing TBG in an intermediate coupling regime. Here we study the phase diagram of TBG in the presence of heterostrain with unbiased, large-scale density matrix renormalization group calculations (bond dimension $χ=24576$), including all spin and valley degrees of freedom. Working at filling $ν= -3$, we find a strain of $0.05\%$ drives a transition from a quantized anomalous Hall insulator into an incommensurate-Kekulé spiral (IKS) phase. This peculiar order, proposed and studied at mean-field level by Kwan et al (PRX 11, 041063), breaks both valley conservation and translation symmetry $\hat{T}$, but preserves a modified translation symmetry $\hat{T}'$ with moiré-incommensurate phase modulation. Even higher strains drive the system to a fully symmetric metal.

cond-mat.str-el↗

arXiv2022

Interacting models for twisted bilayer graphene: a quantum chemistry approach

The nature of correlated states in twisted bilayer graphene (TBG) at the magic angle has received intense attention in recent years. We present a numerical study of an interacting Bistritzer-MacDonald (IBM) model of TBG using a suite of methods in quantum chemistry, including Hartree-Fock, coupled cluster singles, doubles (CCSD), and perturbative triples (CCSD(T)), as well as a quantum chemistry formulation of the density matrix renormalization group method (DMRG). Our treatment of TBG is agnostic to gauge choices, and hence we present a new gauge-invariant formulation to detect the spontaneous symmetry breaking in interacting models. To benchmark our approach, we focus on a simplified spinless, valleyless IBM model. At integer filling ($ν=0$), all numerical methods agree in terms of energy and $C_{2z} \mathcal{T}$ symmetry breaking. Additionally, as part of our benchmarking, we explore the impact of different schemes for removing ``double-counting'' in the IBM model. Our results at integer filling suggest that cross-validation of different IBM models may be needed for future studies of the TBG system. After benchmarking our approach at integer filling, we perform the first systematic study of the IBM model near integer filling (for $|ν|< 0.2$). In this regime, we find that the ground state can be in a metallic and $C_{2z} \mathcal{T}$ symmetry breaking phase. The ground state appears to have low entropy, and therefore can be relatively well approximated by a single Slater determinant. Furthermore, we observe many low entropy states with energies very close to the ground state energy in the near integer filling regime.

cond-mat.str-el↗

arXiv2022

Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene

Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moiré potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are strong. We further elucidate how the inter-valley Hund's coupling determines the spin-structure of the IVC ground state and breaks the degeneracy between spin-singlet and triplet superconductivity. Remarkably, if the normal state is spin-unpolarized, we find that a ferromagnetic Hund's coupling favors spin-singlet superconductivity, in agreement with experiments. Instead, if the normal state is spin-polarized, then IVC fluctuations lead to spin-triplet pairing.

cond-mat.supr-con↗

arXiv2022

Photo-induced Superconductivity = Discrete Time Crystal?

We propose that periodic driving can stabilize a new type of order, "period-doubled superconductivity", in which a superconducting order parameter oscillates at half the frequency of the drive. Despite having a zero time-averaged order parameter, the ordered state exhibits perfect conductivity and a Meissner effect. Our theory predicts that this phase may be realized as the steady state of materials shown to exhibit photo-induced superconductivity. We propose to detect the period-doubled oscillation of the order parameter by utilizing a Josephson junction between a photo-induced superconductor and a conventional superconductor. Our theory can also be realized via parametric driving of cold bosonic atoms in an optical lattice.

cond-mat.supr-con↗

arXiv2022

Skyrmion Superconductivity: DMRG evidence for a topological route to superconductivity

It was recently suggested that the topology of magic-angle twisted bilayer graphene's (MATBG) flat bands could provide a novel mechanism for superconductivity distinct from both weakly-coupled BCS theory and the $d$-wave phenomenology of the high-$T_c$ cuprates. In this work, we examine this possibility using a density matrix renormalization group (DMRG) study of a model which captures the essential features of MATBG's symmetry and topology. Using large scale cylinder-DMRG calculations to obtain the ground state and its excitations as a function of the electron doping, we find clear evidence for superconductivity driven by the binding of electrons into charge-$2e$ skyrmions. Remarkably, this binding is observed even in the regime where the unscreened Coulomb repulsion is by-far the largest energy scale, demonstrating the robustness of this topological, all-electronic pairing mechanism.

cond-mat.str-el↗

arXiv2022

Holographic quantum simulation of entanglement renormalization circuits

While standard approaches to quantum simulation require a number of qubits proportional to the number of simulated particles, current noisy quantum computers are limited to tens of qubits. With the technique of holographic quantum simulation, a $D$-dimensional system can be simulated with a $D{\rm -}1$-dimensional subset of qubits, enabling the study of systems significantly larger than current quantum computers. Using circuits derived from the multiscale entanglement renormalization ansatz (MERA), we accurately prepare the ground state of an $L=32$ critical, non-integrable perturbed Ising model and measure long-range correlations on the 10 qubit Quantinuum trapped ion computer. We introduce generalized MERA (gMERA) networks that interpolate between MERA and matrix product state networks and demonstrate that gMERA can capture far longer correlations than a MERA with the same number of qubits, at the expense of greater circuit depth. Finally, we perform noisy simulations of these two network ansätze and find that the optimal choice of network depends on noise level, available qubits, and the state to be represented.

quant-ph↗

arXiv2021

Field-tuned and zero-field fractional Chern insulators in magic angle graphene

In contrast to the fractional quantum Hall (FQH) effect, where electron density fixes the applied magnetic field, fractional Chern insulators (FCIs) can realize FQH states in comparatively weak or even zero magnetic fields. Previous theoretical work highlighted magic angle graphene as a promising FCI platform, satisfying the twin requirements of flat bands and lowest-Landau-level-like quantum geometry. Indeed, recent experiments have demonstrated FCIs in magic angle graphene with weak magnetic fields. Here we conduct a detailed theoretical study of the most prominent FCI state observed, and clarify the role of the magnetic field in stabilizing this state. We introduce two new technical tools: first, we generalize the notion of ideal quantum geometry to Hofstadter minibands and, second, we extend the Hartree-Fock theory of magic-angle graphene to finite field, to account for the interaction generated bandwidth. We show that magnetic field both dramatically reduces the effective bandwidth and improves the quantum geometry for hosting FCIs. Using density matrix renormalization group (DMRG) simulations of a microscopic model of magic angle graphene, we establish the regime of bandwidth and quantum geometry indicators where FCIs are stabilized. Further characterizing the finite-field bands by the same quantities we show how a zero-field charge density wave state gives way to an FCI state at a magnetic flux consistent with experiment. We also speculate on the other FCIs seen in the same experiments, including anomalous incompressible states and even-denominator fractions which may host non-Abelian states. Finally, when bandwidth is the limiting factor, we propose a range of experimental parameters where FCIs should appear at zero magnetic field.

cond-mat.str-el↗

arXiv2021

Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and spatially non-uniform order. This order, which we dub the 'incommensurate Kekulé spiral' (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries, but preserves a modified translation symmetry $\hat{T}'$ -- which simultaneously shifts the spatial coordinates and rotates the $U(1)$ angle which characterizes the spontaneous inter-valley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

cond-mat.str-el↗

arXiv2021

Detecting symmetry breaking in magic angle graphene using scanning tunneling microscopy

A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade" of spontaneous symmetry breaking transitions, sparking interest in the potential relationship between symmetry-breaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here we show how atomically-resolved scanning tunneling microscopy can be used as a fingerprint of symmetry breaking order. By analyzing the pattern of sublattice polarization and "Kekulé" distortions in small magnetic fields, order parameters for each of the most competitive symmetry-breaking states can be identified. In particular, we show that the "Kramers intervalley coherent state," which theoretical work predicts to be the ground state at even integer fillings, shows a Kekulé distortion which emerges only in a magnetic field.

cond-mat.str-el↗

arXiv2021

A universal tripartite entanglement signature of ungappable edge states

Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this work we show that a multipartite entanglement measure recently proposed in the context of holography, the Markov gap, provides a universal diagnostic of ungappable edge states. Defined as a difference of the reflected entropy and mutual information $h(A:B) = S_R(A:B) - I(A:B)$ between two parties, we argue that for $A,B$ being adjacent subregions in the bulk, $h=\frac{c_+}{3}\log 2$, where $c_+$ is the minimal total central charge of the boundary theory. As evidence, we prove that $h=0$ for string-net models, and numerically verify that $h=\frac{|C|}{3}\log 2$ for a Chern-$C$ insulator. Our work establishes a unique bulk entanglement criteria for the presence of a conformal field theory on the boundary.

quant-ph↗

arXiv2021

Performance of the rigorous renormalization group for first order phase transitions and topological phases

Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in 1D systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau et al. [Nature Physics 11, 566 (2015)]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first order phase transitions and in symmetry protected topological phases. Our study is motived by the question of when RRG might provide a useful complement to the more established DMRG technique. In particular, despite its general utility, DMRG can give unreliable results near first order phase transitions and in topological phases, since its local update procedure can fail to adequately explore (near) degenerate manifolds. The rigorous theoretical underpinnings of RRG, meanwhile, suggest that it should not suffer from the same difficulties. We show this optimism is justified, and that RRG indeed determines accurate, well-ordered energies even when DMRG does not. Moreover, our performance analysis indicates that in certain circumstances seeding DMRG with states determined by coarse runs of RRG may provide an advantage over simply performing DMRG.

cond-mat.str-el↗

arXiv2021

Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic phases (QHFM), with broken spin or valley symmetry. Visualizing atomic scale electronic wavefunctions with scanning tunneling spectroscopy (STS), we resolve microscopic signatures of valley ordering in QHFM and fractional quantum Hall phases of graphene. At charge neutrality, we observe a field-tuned continuous quantum phase transition from a valley polarized state to an intervalley coherent state, with a Kekule distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekule phase, we visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley ordered phases and their topological excitations in a wide range of materials.

cond-mat.mes-hall↗

arXiv2021

Correlated interlayer exciton insulator in double layers of monolayer WSe2 and moiré WS2/WSe2

Moiré superlattices in van der Waals heterostructures have emerged as a powerful tool for engineering novel quantum phenomena. Here we report the observation of a correlated interlayer exciton insulator in a double-layer heterostructure composed of a WSe2 monolayer and a WS2/WSe2 moiré bilayer that are separated by an ultrathin hexagonal boron nitride (hBN). The moiré WS2/WSe2 bilayer features a Mott insulator state at hole density p/p0 = 1, where p0 corresponds to one hole per moiré lattice site. When electrons are added to the Mott insulator in the WS2/WSe2 moiré bilayer and an equal number of holes are injected into the WSe2 monolayer, a new interlayer exciton insulator emerges with the holes in the WSe2 monolayer and the electrons in the doped Mott insulator bound together through interlayer Coulomb interactions. The excitonic insulator is stable up to a critical hole density of ~ 0.5p0 in the WSe2 monolayer, beyond which the system becomes metallic. Our study highlights the opportunities for realizing novel quantum phases in double-layer moiré systems due to the interplay between the moiré flat band and strong interlayer electron interactions.

cond-mat.mes-hall↗

arXiv2021

Topological charge density waves at half-integer filling of a moiré superlattice

At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and Hofstadter bands; in both cases, a large magnetic field is required to engineer the underlying flat band. The recent observation of quantum anomalous Hall effects (QAH) in narrow band moiré systems has led to the theoretical prediction that such phases may be realized even at zero magnetic field. Here we report the experimental observation of insulators with Chern number $C=1$ in the zero magnetic field limit at $ν=3/2$ and $7/2$ filling of the moiré superlattice unit cell in twisted monolayer-bilayer graphene (tMBG). Our observation of Chern insulators at half-integer values of $ν$ suggests spontaneous doubling of the superlattice unit cell, in addition to spin- and valley-ferromagnetism. This is confirmed by Hartree-Fock calculations, which find a topological charge density wave ground state at half filling of the underlying $C=2$ band, in which the Berry curvature is evenly partitioned between occupied and unoccupied states. We find the translation symmetry breaking order parameter is evenly distributed across the entire folded superlattice Brillouin zone, suggesting that the system is in the flat band, strongly correlated limit. Our findings show that the interplay of quantum geometry and Coulomb interactions in moiré bands allows for topological phases at fractional superlattice filling that spontaneously break time-reversal symmetry, a prerequisite in pursuit of zero magnetic field phases harboring fractional statistics as elementary excitations or bound to lattice dislocations.

cond-mat.str-el↗

arXiv2021

Visualizing delocalized correlated electronic states in twisted double bilayer graphene

The discovery of interaction-driven insulating and superconducting phases in moiré van der Waals heterostructures has sparked considerable interest in understanding the novel correlated physics of these systems. While a significant number of studies have focused on twisted bilayer graphene, correlated insulating states and a superconductivity-like transition up to 12 K have been reported in recent transport measurements of twisted double bilayer graphene. Here we present a scanning tunneling microscopy and spectroscopy study of gate-tunable twisted double bilayer graphene devices. We observe splitting of the van Hove singularity peak by ~20 meV at half-filling of the conduction flat band, with a corresponding reduction of the local density of states at the Fermi level. By mapping the tunneling differential conductance we show that this correlated system exhibits energetically split states that are spatially delocalized throughout the different regions in the moiré unit cell, inconsistent with order originating solely from onsite Coulomb repulsion within strongly-localized orbitals. We have performed self-consistent Hartree-Fock calculations that suggest exchange-driven spontaneous symmetry breaking in the degenerate conduction flat band is the origin of the observed correlated state. Our results provide new insight into the nature of electron-electron interactions in twisted double bilayer graphene and related moiré systems.

cond-mat.str-el↗

arXiv2021

Universal tripartite entanglement in one-dimensional many-body systems

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross-section, we introduce two related non-negative measures of tripartite entanglement $g$ and $h$. We prove structure theorems which show that states with nonzero $g$ or $h$ have nontrivial tripartite entanglement. We then establish that in 1D these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either $g\neq 0$ and $h=0$ or $g=h=0$, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing $g$ and $h$ from a lattice model. We compute $g$ and $h$ for various CFTs and show that $h$ depends only on the central charge whereas $g$ depends on the whole operator content.

quant-ph↗

arXiv2021

Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene

Spontaneous symmetry breaking plays a pivotal role in many areas of physics, engendering a variety of excitations from sound modes in solids to pions in nuclear physics. Equally important excitations are solitons, nonlinear configurations of the symmetry breaking field, which can enjoy exceptional stability as in the Skyrme model of nuclear forces. Here we argue that similar models may describe magic angle graphene, a remarkable new material . When the angle between two sheets of graphene is near the magic angle of $\sim 1^\circ$, insulating behavior is observed, which gives way to superconductivity on changing the electron density. We propose a unifying description of both the order underlying the insulator as well as the superconductor. While the symmetry breaking condensate leads to the ordered phase, topological solitons in the condensate - skyrmions - are shown to be bosons that carry an electric charge of 2e. Condensation of skyrmions leads to a superconductor whose pairing strength, symmetry and other properties are inferred. More generally, we show how topological textures can mitigate Coulomb repulsion to pair electrons and provide a new route to superconductivity. Our mechanism potentially applies to much wider class of systems but crucially invokes certain key ingredient such as inversion symmetry present in magic angle graphene. We discuss how these insights not only clarify why certain correlated moire materials do not superconduct, they also point to promising new platforms where robust superconductivity is anticipated.

cond-mat.str-el↗

arXiv2021

Preparation of Low Entropy Correlated Many-body States via Conformal Cooling Quenches

We analyze a method for preparing low-entropy many-body states in isolated quantum optical systems of atoms, ions and molecules. Our approach is based upon shifting entropy between different regions of a system by spatially modulating the magnitude of the effective Hamiltonian. We conduct two case studies, on a topological spin chain and the spinful fermionic Hubbard model, focusing on the key question: can a "conformal cooling quench" remove sufficient entropy within experimentally accessible timescales? Finite temperature, time-dependent matrix product state calculations reveal that even moderately sized "bath" regions can remove enough energy and entropy density to expose coherent low temperature physics. The protocol is particularly natural in systems with long-range interactions such lattice-trapped polar molecules and Rydberg dressed atoms where the magnitude of the Hamiltonian scales directly with the density. To this end, we propose a simple implementation of conformal cooling quenches in a dilutely-filled optical lattice, where signatures of quantum magnetism can be observed.

cond-mat.quant-gas↗