arXiv subjects

Rhine Samajdar

Publications and source records attributed to Rhine Samajdar.

At least 55 records · Page 3Linked to original sources

arXiv2021

Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array

Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a comprehensive theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we identify several first-order and continuous phase transitions by performing large-scale quantum Monte Carlo simulations and develop an analytical understanding of the nature of these transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that under open boundary conditions, the boundary itself undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important new insights into both the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.

quant-ph↗

arXiv2021

Machine learning discovery of new phases in programmable quantum simulator snapshots

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lend to the possibility of automatically discovering structures in experimental datasets that manual inspection may miss. Here, we introduce an interpretable unsupervised-supervised hybrid machine learning approach, the hybrid-correlation convolutional neural network (Hybrid-CCNN), and apply it to experimental data generated using a programmable quantum simulator based on Rydberg atom arrays. Specifically, we apply Hybrid-CCNN to analyze new quantum phases on square lattices with programmable interactions. The initial unsupervised dimensionality reduction and clustering stage first reveals five distinct quantum phase regions. In a second supervised stage, we refine these phase boundaries and characterize each phase by training fully interpretable CCNNs and extracting the relevant correlations for each phase. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase capture quantum fluctuations in the striated phase and identify two previously undetected phases, the rhombic and boundary-ordered phases. These observations demonstrate that a combination of programmable quantum simulators with machine learning can be used as a powerful tool for detailed exploration of correlated quantum states of matter.

quant-ph↗

arXiv2021

Phonon Hall viscosity from phonon-spinon interactions

Motivated by experimental observations, Samajdar et al. [Nature Physics 15, 1290 (2019)] have proposed that the insulating Neel state in the parent compounds of the cuprates is proximate to a quantum phase transition to a state in which Neel order coexists with semion topological order. We study the manner in which proximity to this transition can make the phonons chiral, by inducing a significant phonon Hall viscosity. We describe the spinon-phonon coupling in a lattice spinon model coupled to a strain field, and also using a general continuum theory constrained only by symmetry. We find a nonanalytic Hall viscosity across the transition, with a divergent second derivative at zero temperature.

cond-mat.str-el↗

arXiv2021

Electric-field-tunable electronic nematic order in twisted double-bilayer graphene

Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the nematic phase of tDBG and its experimental manifestations. First, we perform a detailed comparison between the theoretically calculated local density of states and recent scanning tunneling microscopy data [arXiv:2009.11645] to resolve the internal structure of the nematic order parameter in terms of the layer, sublattice, spin, and valley degrees of freedom. We find strong evidence that the dominant contribution to the nematic order parameter comes from states at the moiré scale rather than at the microscopic scale of the individual graphene layers, which demonstrates the key role played by the moiré degrees of freedom and confirms the correlated nature of the nematic phase in tDBG. Secondly, our analysis reveals an unprecedented tunability of the orientation of the nematic director in tDBG by an externally applied electric field, allowing the director to rotate away from high-symmetry crystalline directions. We compute the expected fingerprints of this rotation in both STM and transport experiments, providing feasible ways to probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the displacement field, this effect opens an interesting route to the electrostatic control of electronic nematicity in moiré systems.

cond-mat.str-el↗

arXiv2021

Probing Topological Spin Liquids on a Programmable Quantum Simulator

Quantum spin liquids, exotic phases of matter with topological order, have been a major focus of explorations in physical science for the past several decades. Such phases feature long-range quantum entanglement that can potentially be exploited to realize robust quantum computation. We use a 219-atom programmable quantum simulator to probe quantum spin liquid states. In our approach, arrays of atoms are placed on the links of a kagome lattice and evolution under Rydberg blockade creates frustrated quantum states with no local order. The onset of a quantum spin liquid phase of the paradigmatic toric code type is detected by evaluating topological string operators that provide direct signatures of topological order and quantum correlations. Its properties are further revealed by using an atom array with nontrivial topology, representing a first step towards topological encoding. Our observations enable the controlled experimental exploration of topological quantum matter and protected quantum information processing.

quant-ph↗

arXiv2020

Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator

Motivated by far-reaching applications ranging from quantum simulations of complex processes in physics and chemistry to quantum information processing, a broad effort is currently underway to build large-scale programmable quantum systems. Such systems provide unique insights into strongly correlated quantum matter, while at the same time enabling new methods for computation and metrology. Here, we demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms, featuring strong interactions controlled via coherent atomic excitation into Rydberg states. Using this approach, we realize a quantum spin model with tunable interactions for system sizes ranging from 64 to 256 qubits. We benchmark the system by creating and characterizing high-fidelity antiferromagnetically ordered states, and demonstrate the universal properties of an Ising quantum phase transition in (2+1) dimensions. We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation, experimentally map the phase diagram, and investigate the role of quantum fluctuations. Offering a new lens into the study of complex quantum matter, these observations pave the way for investigations of exotic quantum phases, non-equilibrium entanglement dynamics, and hardware-efficient realization of quantum algorithms.

quant-ph↗

arXiv2020

Quantum phases of Rydberg atoms on a kagome lattice

We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a novel regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays.

cond-mat.quant-gas↗

arXiv2020

Universal moiré nematic phase in twisted graphitic systems

Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron-electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report scanning tunneling microscopy (STM) measurements that reveal the existence of threefold rotational (C3) symmetry breaking in twisted double bilayer graphene (tDBG). Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the C3 symmetry breaking cannot be explained by heterostrain or the displacement field, and is instead a manifestation of an interaction-driven electronic nematic phase, which emerges even away from integer fillings. Comparing our experimental data with a combination of microscopic and phenomenological modeling, we show that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moiré lattice, pointing to the universal character of this ordered state in flat band moiré materials.

cond-mat.str-el↗

arXiv2020

Unquantized thermal Hall effect in quantum spin liquids with spinon Fermi surfaces

Recent theoretical studies have found quantum spin liquid states with spinon Fermi surfaces upon the application of a magnetic field on a gapped state with topological order. We investigate the thermal Hall conductivity across this transition, describing how the quantized thermal Hall conductivity of the gapped state changes to an unquantized thermal Hall conductivity in the gapless spinon Fermi surface state. We consider two cases, both of potential experimental interest: the state with non-Abelian Ising topological order on the honeycomb lattice, and the state with Abelian chiral spin liquid topological order on the triangular lattice.

cond-mat.str-el↗

arXiv2020

Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene

Starting from a continuum-model description, we develop a microscopic weak-coupling theory for superconductivity in twisted double-bilayer graphene. We study both electron-phonon and entirely electronic pairing mechanisms. In each case, the leading superconducting instability transforms under the trivial representation, $A$, of the point group $C_3$ of the system, while the subleading pairing phases belong to the $E$ channel. We explicitly compute the momentum dependence of the associated order parameters and find that the leading state has no nodal points for electron-phonon pairing but exhibits six sign changes on the Fermi surface if the Coulomb interaction dominates. On top of these system-specific considerations, we also present general results relevant to other correlated graphene-based moiré superlattice systems. We show that, irrespective of microscopic details, triplet pairing will be stabilized if the collective electronic fluctuations breaking the enhanced $\text{SU}(2)_+ \times \text{SU}(2)_-$ spin symmetry of these systems are odd under time reversal, even when the main $\text{SU}(2)_+ \times \text{SU}(2)_-$-symmetric part of the pairing glue is provided by phonons. Furthermore, we discuss the disorder sensitivity of the candidate pairing states and demonstrate that the triplet phase is protected against disorder on the moiré scale.

cond-mat.supr-con↗

arXiv2020

Pairing in graphene-based moiré superlattices

We present a systematic classification and analysis of possible pairing instabilities in graphene-based moiré superlattices. Motivated by recent experiments on twisted double-bilayer graphene showing signs of triplet superconductivity, we analyze both singlet and triplet pairing separately, and describe how these two channels behave close to the limit where the system is invariant under separate spin rotations in the two valleys, realizing an SU(2)$_+$ $\times$ SU(2)$_-$ symmetry. Further, we discuss the conditions under which singlet and triplet can mix via two nearly degenerate transitions, and how the different pairing states behave when an external magnetic field is applied. The consequences of the additional microscopic or emergent approximate symmetries relevant for superconductivity in twisted bilayer graphene and ABC trilayer graphene on hexagonal boron nitride are described in detail. We also analyze which of the pairing states can arise in mean-field theory and study the impact of corrections coming from ferromagnetic fluctuations. For instance, we show that, close to the parameters of mean-field theory, a nematic mixed singlet-triplet state emerges. Our study illustrates that graphene superlattices provide a rich platform for exotic superconducting states, and allow for the admixture of singlet and triplet pairing even in the absence of spin-orbit coupling.

cond-mat.supr-con↗

arXiv2020

Gauge Theories for the Thermal Hall Effect

We consider the thermal Hall effect of fermionic matter coupled to emergent gauge fields in 2+1 dimensions. While the low-temperature thermal Hall conductivity of bulk topological phases can be connected to chiral edge states and a gravitational anomaly, there is no such interpretation at nonzero temperatures above 2+1 dimensional quantum critical points. In the limit of a large number of matter flavors, the leading contribution to the thermal Hall conductivity is that from the fermionic matter. The next-to-leading contribution is from the gauge fluctuations, and this has a sign which is opposite to that of the matter contribution. We illustrate this by computations on a Dirac Chern-Simons theory of the quantum phase transition in a square-lattice antiferromagnet involving the onset of semion topological order. We find similar results for a model of the pseudogap metal with Fermi pockets coupled to an emergent U(1) gauge field. We note connections to recent observations on the hole-doped cuprates: our theory captures the main trends, but the overall magnitude of the effect is smaller than that observed.

cond-mat.str-el↗

arXiv2020

Complex density wave orders and quantum phase transitions in a model of square-lattice Rydberg atom arrays

We describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.

cond-mat.str-el↗

arXiv2019

Enhanced thermal Hall effect in the square-lattice Néel state

Recent experiments on several cuprate compounds have identified an enhanced thermal Hall response in the pseudogap phase. Most strikingly, this enhancement persists even in the undoped system, which challenges our understanding of the insulating parent compounds. To explain these surprising observations, we study the quantum phase transition of a square-lattice antiferromagnet from a confining Néel state to a state with coexisting Néel and semion topological order. The transition is driven by an applied magnetic field and involves no change in the symmetry of the state. The critical point is described by a strongly-coupled conformal field theory with an emergent global $SO(3)$ symmetry. The field theory has four different formulations in terms of $SU(2)$ or $U(1)$ gauge theories, which are all related by dualities; we relate all four theories to the lattice degrees of freedom. We show how proximity of the confining Néel state to the critical point can explain the enhanced thermal Hall effect seen in experiment.

cond-mat.str-el↗

arXiv2019

Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study

Motivated by recent transport measurements in high-$T_c$ cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field ansätze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any $T>0$, also show a similarly enhanced thermal Hall conductivity.

cond-mat.str-el↗

arXiv2019

Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator

Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. While time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early universe to Bose Einstein Condensates, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is an outstanding challenge. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models, providing new insights into exotic systems that have not been understood previously, and opening the door for precision studies of critical phenomena, simulations of lattice gauge theories and applications to quantum optimization.

quant-ph↗

arXiv2018

Quantum field theory for the chiral clock transition in one spatial dimension

We describe the quantum phase transition in the $N$-state chiral clock model in spatial dimension $d=1$. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global $\mathbb{Z}_N$ symmetry, to a gapped phase with the $\mathbb{Z}_N$ symmetry restored. The transition has dynamical critical exponent $z \neq 1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single boson condensate in the background of a higher-dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2-d$, with $4-N$ chosen to be of order $2-d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $ν$.

cond-mat.str-el↗

arXiv2018

Numerical study of the chiral $\mathbb{Z}_3$ quantum phase transition in one spatial dimension

Recent experiments on a one-dimensional chain of trapped alkali atoms [arXiv:1707.04344] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous $\mathbb{Z}_3$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley $et\, \,al.$ [arXiv:cond-mat/0309438]. By symmetry arguments, the transition is expected to be in the universality class of the $\mathbb{Z}_3$ chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order-disorder transition in these models, and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $ν$. Our analysis presents the only known instance of a strongly-coupled transition between gapped states with $z \ne 1$, implying an underlying nonconformal critical field theory.

cond-mat.str-el↗