Gbadebo Taofeek Yusuf, Sukhwinder Singh, Alexandros Askounis, Zlatka Stoeva, Fideline Tchuenbou-Magaia
Grain-boundary-limited charge transport remains a key bottleneck in polycrystalline thermoelectric materials, where reduced carrier mobility degrades electrical conductivity and suppresses the power factor. Here we present a semi-empirical mobility model that integrates three dominant grain-boundary mechanisms: (i) weighted mobility linked to carrier effective mass and concentration, (ii) thermionic emission across grain-boundary barriers, and (iii) geometric suppression arising from a finite mean free path ($\ell$). The model is validated against a diverse set of polycrystalline thermoelectric materials -- including Bi$_2$Te$_3$, PbTe, Mg$_2$Si, and SnSe -- showing excellent agreement with experiment ($R^2 = 0.93$--0.99) and yielding physically consistent parameters: $0 \lesssim Φ_{\mathrm{GB}} \lesssim 0.15$ eV and $\ell \approx 15$--60 nm. The model captures the non-monotonic mobility trends produced by the interplay between barrier activation and phonon scattering. We further apply the model to Al-doped ZnO, revealing that combined grain-boundary passivation (reducing $Φ_{\mathrm{GB}}$ from 0.15 eV to 0.05 eV) and moderate grain growth (increasing $\ell$ from 5 nm to 25 nm) can raise the power factor by $\sim 6\times$ (from $\sim 4$ to $\sim 26$ mW\,m$^{-1}$\,K$^{-2}$) and the electronic quality factor $B$ by nearly $7\times$ (from $\sim 0.15$ to $>1.0 \times 10^{-3}$ m$^2$\,V$^{-1}$\,s$^{-1}$\,kg$^{3/2}$), approaching values achieved in leading chalcogenide thermoelectrics. The model therefore provides a transparent and practical framework for grain-boundary engineering in oxide-based thermoelectrics.
Sukhwinder Singh, Robert N. C. Pfeifer, Guifre Vidal
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to incorporate a global internal symmetry, given by a compact, completely reducible group G, into tensor network decompositions and algorithms. Here we specialize to the case of Abelian groups and, for concreteness, to a U(1) symmetry, often associated with particle number conservation. We consider tensor networks made of tensors that are invariant (or covariant) under the symmetry, and explain how to decompose and manipulate such tensors in order to exploit their symmetry. In numerical calculations, the use of U(1) symmetric tensors allows selection of a specific number of particles, ensures the exact preservation of particle number, and significantly reduces computational costs. We illustrate all these points in the context of the multi-scale entanglement renormalization ansatz.
Sukhwinder Singh, Guifre Vidal
The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with a given particle number or spin), to ensure the exact preservation of total charge, and to significantly reduce computational costs. Compared to the case of a generic tensor network, the practical implementation of symmetries in the MPS is simplified by the fact that tensors only have three indices (they are trivalent, just as the Clebsch-Gordan coefficients of the symmetry group) and are organized as a one-dimensional array of tensors, without closed loops. Instead, a more complex tensor network, one where tensors have a larger number of indices and/or a more elaborate network structure, requires a more general treatment. In two recent papers, namely (i) [Phys. Rev. A 82, 050301 (2010)] and (ii) [Phys. Rev. B 83, 115125 (2011)], we described how to incorporate a global internal symmetry into a generic tensor network algorithm based on decomposing and manipulating tensors that are invariant under the symmetry. In (i) we considered a generic symmetry group G that is compact, completely reducible and multiplicity free, acting as a global internal symmetry. Then in (ii) we described the practical implementation of Abelian group symmetries. In this paper we describe the implementation of non-Abelian group symmetries in great detail and for concreteness consider an SU(2) symmetry. Our formalism can be readily extended to more exotic symmetries associated with conservation of total fermionic or anyonic charge. As a practical demonstration, we describe the SU(2)-invariant version of the multi-scale entanglement renormalization ansatz and apply it to study the low energy spectrum of a quantum spin chain with a global SU(2) symmetry.
Gholamreza Kakamanshadi, Savita Gupta, Sukhwinder Singh
A wireless sensor network consists of several sensor nodes. Sensor nodes collaborate to collect meaningful environmental information and send them to the base station. During these processes, nodes are prone to failure, due to the energy depletion, hardware or software failure, etc. Therefore, fault tolerance and energy efficiency are two important objectives for reliable packet delivery. To address these objectives a novel method called fuzzy informer homed routing protocol is introduced. The proposed method tries to distribute the workload between every sensor node. A fuzzy logic approach is used to handle uncertainties in cluster head communication range estimation. The simulation results show that the proposed method can significantly reduce energy consumption as compared with IHR and DHR protocols. Furthermore, results revealed that it performs better than IHR and DHR protocols in terms of first node dead and half of the nodes alive, throughput and total remaining energy. It is concluded that the proposed protocol is a stable and energy efficient fault tolerance algorithm for wireless sensor networks.
Sukhwinder Singh, Robert N. C. Pfeifer, Guifre Vidal, Gavin K. Brennen
Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved topological charges and collectively carry non-local degrees of freedom. In this paper we extend the formalism of MPS to lattice systems of anyons. The anyonic MPS is constructed from tensors that explicitly conserve topological charge. We describe how to adapt the time-evolving block decimation (TEBD) algorithm to the anyonic MPS in order to simulate dynamics under a local and charge-conserving Hamiltonian. To demonstrate the effectiveness of anyonic TEBD algorithm, we used it to simulate (i) the ground state (using imaginary time evolution) of an infinite 1D critical system of (a) Ising anyons and (b) Fibonacci anyons both of which are well studied, and (ii) the real time dynamics of an anyonic Hubbard-like model of a single Ising anyon hopping on a ladder geometry with an anyonic flux threading each island of the ladder. Our results pertaining to (ii) give insight into the transport properties of anyons. The anyonic MPS formalism can be readily adapted to study systems with conserved symmetry charges, as this is equivalent to a specialization of the more general anyonic case.
Sukhwinder Singh, Gavin K. Brennen
Jun 16, 2016·quant-ph·PDF Wavelets encode data at multiple resolutions, which in a wavelet description of a quantum field theory, allows for fields to carry, in addition to space-time coordinates, an extra dimension: scale. A recently introduced Exact Holographic Mapping [C.H. Lee and X.-L. Qi, Phys. Rev. B 93, 035112 (2016)] uses the Haar wavelet basis to represent the free Dirac fermionic quantum field theory (QFT) at multiple renormalization scales thereby inducing an emergent bulk geometry in one higher dimension. This construction is, in fact, generic and we show how higher families of Daubechies wavelet transforms of 1+1 dimensional scalar bosonic QFT generate a bulk description with a variable rate of renormalization flow. In the massless case, where the boundary is described by conformal field theory, the bulk correlations decay with distance consistent with an Anti-de-Sitter space (AdS3) metric whose radius of curvature depends on the wavelet family used. We propose an experimental demonstration of the bulk/boundary correspondence via a digital quantum simulation using Gaussian operations on a set of quantum harmonic oscillator modes.
Sujith Pulikodan, Abhayjeet Singh, Agneedh Basu, Nihar Desai, Pavan Kumar J, Pranav D Bhat, Raghu Dharmaraju, Ritika Gupta, Sathvik Udupa, Saurabh Kumar, Sumit Sharma, Vaibhav Vishwakarma, Visruth Sanka, Dinesh Tewari, Harsh Dhand, Amrita Kamat, Sukhwinder Singh, Shikhar Vashishth, Partha Talukdar, Raj Acharya, Prasanta Kumar Ghosh
Project VAANI is an initiative to create an India-representative multi-modal dataset that comprehensively maps India's linguistic diversity, starting with 165 districts across the country in its first two phases. Speech data is collected through a carefully structured process that uses image-based prompts to encourage spontaneous responses. Images are captured through a separate process that encompasses a broad range of topics, gathered from both within and across districts. The collected data undergoes a rigorous multi-stage quality evaluation, including both automated and manual checks to ensure highest possible standards in audio quality and transcription accuracy. Following this thorough validation, we have open-sourced around 289K images, approximately 31,270 hours of audio recordings, and around 2,067 hours of transcribed speech, encompassing 112 languages from 165 districts from 31 States and Union territories. Notably, significant of these languages are being represented for the first time in a dataset of this scale, making the VAANI project a groundbreaking effort in preserving and promoting linguistic inclusivity. This data can be instrumental in building inclusive speech models for India, and in advancing research and development across speech, image, and multimodal applications.
Sukhwinder Singh, Guifre Vidal
Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multi-scale entanglement renormalization ansatz (MERA), a tensor network capable of efficiently describing a large class of many-body ground states, including those of systems at a quantum critical point or with topological order. The MERA has also been proposed to be a discrete realization of the holographic principle of string theory. In this paper we propose the use of symmetric tensors as a mechanism to build a symmetry protected RG flow, and discuss two important applications of this construction. First, we argue that symmetry protected entanglement renormalization produces the proper structure of RG fixed-points, namely a fixed-point for each symmetry protected phase. Second, in the context of holography, we show that by using symmetric tensors, a global symmetry at the boundary becomes a local symmetry in the bulk, thus explicitly realizing in the MERA a characteristic feature of the AdS/CFT correspondence.
Sukhwinder Singh, Nathan A. McMahon, Gavin K. Brennen
In the holographic correspondence of quantum gravity, a global onsite symmetry at the boundary generally translates to a local gauge symmetry in the bulk. We describe one way how the global boundary onsite symmetries can be gauged within the formalism of the multi-scale renormalization ansatz (MERA), in light of the ongoing discussion between tensor networks and holography. We describe how to "lift" the MERA representation of the ground state of a generic one dimensional (1D) local Hamiltonian, which has a global onsite symmetry, to a dual quantum state of a 2D "bulk" lattice on which the symmetry appears gauged. The 2D bulk state decomposes in terms of spin network states, which label a basis in the gauge-invariant sector of the bulk lattice. This decomposition is instrumental to obtain expectation values of gauge-invariant observables in the bulk, and also reveals that the bulk state is generally entangled between the gauge and the remaining ("gravitational") bulk degrees of freedom that are not fixed by the symmetry. We present numerical results for ground states of several 1D critical spin chains to illustrate that the bulk entanglement potentially depends on the central charge of the underlying conformal field theory. We also discuss the possibility of emergent topological order in the bulk using a simple example, and also of emergent symmetries in the non-gauge ("gravitational") sector in the bulk. More broadly, our holographic model translates the MERA, a tensor network state, to a superposition of spin network states, as they appear in lattice gauge theories in one higher dimension.
Sukhwinder Singh
Mar 10, 2012·quant-ph·PDF In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our formalism is independent of the details of a specific tensor network decomposition since the symmetry constraints are imposed at the level of individual tensors. Moreover, the formalism can be applied to a wide spectrum of physical symmetries described by any discrete or continuous group that is compact and reducible. We describe in detail the implementation of the conservation of total particle number (U(1) symmetry) and of total angular momentum (SU(2) symmetry). Our formalism can also be readily generalized to incorporate more exotic symmetries such as conservation of total charge in anyonic systems.
Sukhwinder Singh
Given a local gapped Hamiltonian with a global symmetry on a one dimensional lattice we describe a method to identify if the Hamiltonian belongs to a quantum phase in which the symmetry is spontaneously broken in the ground states or to a specific symmetry protected phase, without using local or string order parameters. We obtain different matrix product state (MPS) descriptions of the symmetric ground state(s) of the Hamiltonian by restricting the MPS matrices to transform under different projective representations of the symmetry. The phase of the Hamiltonian is identified by examining which MPS descriptions, if any, are injective, namely, whether the largest eigenvalue of the "transfer matrix" obtained from the MPS is unique. We demonstrate the method for translation invariant Hamiltonians with a global SO(3), Z_2 and Z_2 x Z_2 symmetry on an infinite chain.
Zizhu Wang, Sukhwinder Singh, Miguel Navascués
Aug 11, 2016·quant-ph·PDF We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori, since, as we show, there exist instances of local separable states (classical boxes) which admit only entangled (nonclassical) TI extensions. We provide a simple characterization of the set of local states of multiseparable TI spin chains and construct a family of linear witnesses which can detect entanglement in infinite TI states from the nearest-neighbor reduced density matrix. Similarly, we prove that the set of classical TI boxes forms a polytope and devise a general procedure to generate all Bell inequalities which characterize it. Using an algorithm based on matrix product states, we show how some of them can be violated by distant parties conducting identical measurements on an infinite TI quantum state. All our results can be easily adapted to detect entanglement and nonlocality in large (finite, not TI) 1D condensed matter systems.
Sukhwinder Singh, Robert N. C. Pfeifer, Guifre Vidal
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance also in the context of tensor network algorithms, thus setting the stage for cross-fertilization between these two areas of research.
Sukhwinder Singh, Guifre Vidal
Tensor networks offer a variational formalism to efficiently represent wave-functions of extended quantum many-body systems on a lattice. In a tensor network N, the dimension χof the bond indices that connect its tensors controls the number of variational parameters and associated computational costs. In the absence of any symmetry, the minimal bond dimension χ^{min} required to represent a given many-body wave-function |Ψ> leads to the most compact, computationally efficient tensor network description of |Ψ>. In the presence of a global, on-site symmetry, one can use a tensor network N_{sym} made of symmetric tensors. Symmetric tensors allow to exactly preserve the symmetry and to target specific quantum numbers, while their sparse structure leads to a compact description and lowers computational costs. In this paper we explore the trade-off between using a tensor network N with minimal bond dimension χ^{min} and a tensor network N_{sym} made of symmetric tensors, where the minimal bond dimension χ^{min}_{sym} might be larger than χ^{min}. We present two technical results. First, we show that in a tree tensor network, which is the most general tensor network without loops, the minimal bond dimension can always be achieved with symmetric tensors, so that χ^{min}_{sym} = χ^{min}. Second, we provide explicit examples of tensor networks with loops where replacing tensors with symmetric ones necessarily increases the bond dimension, so that χ_{sym}^{min} > χ^{min}. We further argue, however, that in some situations there are important conceptual reasons to prefer a tensor network representation with symmetric tensors (and possibly larger bond dimension) over one with minimal bond dimension.
Nora Tischler, Mathieu L. Juan, Sukhwinder Singh, Xavier Zambrana-Puyalto, Xavier Vidal, Gavin Brennen, Gabriel Molina-Terriza
We motivate metrology schemes based on topological singularities as a way to build robustness against deformations of the system. In particular, we relate reference settings of metrological systems to topological singularities in the measurement outputs. As examples we discuss optical nano-position sensing (i) using a balanced photodetector and a quadrant photodetector, and (ii) a more general image based scheme. In both cases the reference setting is a scatterer position that corresponds to a topological singularity in an output space constructed from the scattered field intensity distributions.
Gavin K. Brennen, Peter Rohde, Barry C. Sanders, Sukhwinder Singh
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis---a multi-scale description of the theory. Since wavelets are compact wavefunctions, this encoding allows for quantum simulations to create particle excitations with compact support and provides a natural way to associate observables in the theory to finite resolution detectors. We show that the wavelet basis is well suited to compute subsystem entanglement entropy by dividing the field into contributions from short-range wavelet degrees of freedom and long-range scale degrees of freedom, of which the latter act as renormalized modes which capture the essential physics at a renormalization fixed point.
Robert N. C. Pfeifer, Glen Evenbly, Sukhwinder Singh, Guifre Vidal
A fundamental process in the implementation of any numerical tensor network algorithm is that of contracting a tensor network. In this process, a network made up of multiple tensors connected by summed indices is reduced to a single tensor or a number by evaluating the index sums. This article presents a MATLAB function ncon(), or "Network CONtractor", which accepts as its input a tensor network and a contraction sequence describing how this network may be reduced to a single tensor or number. As its output it returns that single tensor or number. The function ncon() may be obtained by downloading the source of this preprint.
Robert N. C. Pfeifer, Sukhwinder Singh
The numerical study of anyonic systems is known to be highly challenging due to their non-bosonic, non-fermionic particle exchange statistics, and with the exception of certain models for which analytical solutions exist, very little is known about their collective behaviour as a result. Meanwhile, the density matrix renormalisation group (DMRG) algorithm is an exceptionally powerful numerical technique for calculating the ground state of a low-dimensional lattice Hamiltonian, and has been applied to the study of bosonic, fermionic, and group-symmetric systems. The recent development of a tensor network formulation for anyonic systems opened up the possibility of studying these systems using algorithms such as DMRG, though this has proved challenging both in terms of programming complexity and computational cost. This paper presents the implementation of DMRG for finite anyonic systems, including a detailed scheme for the implementation of anyonic tensors with optimal scaling of computational cost. The anyonic DMRG algorithm is demonstrated by calculating the ground state energy of the Golden Chain, which has become the benchmark system for the numerical study of anyons, and is shown to produce results comparable to those of the anyonic TEBD algorithm and superior to the variationally optimised anyonic MERA, at far lesser computational cost.
Sukhwinder Singh
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"---a correspondence between quantum many-body states mediated by tensor networks as we describe---to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
Babatunde M. Ayeni, Sukhwinder Singh, Robert N. C. Pfeifer, Gavin K. Brennen
Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically tractable, much of the physics of anyons remain still unexplored. In this paper, we show how U(1)-symmetry can be combined with the previously proposed anyonic Matrix Product States to simulate ground states and dynamics of anyonic systems on a lattice at any rational particle number density. We provide proof of principle by studying itinerant anyons on a one dimensional chain where no natural notion of braiding arises and also on a two-leg ladder where the anyons hop between sites and possibly braid. We compare the result of the ground state energies of Fibonacci anyons against hardcore bosons and spinless fermions. In addition, we report the entanglement entropies of the ground states of interacting Fibonacci anyons on a fully filled two-leg ladder at different interaction strength, identifying gapped or gapless points in the parameter space. As an outlook, our approach can also prove useful in studying the time dynamics of a finite number of nonabelian anyons on a finite two-dimensional lattice.