arXiv subjects

Anirban Mukherjee

Publications and source records attributed to Anirban Mukherjee.

47 records · Page 3Linked to original sources

arXiv2021

Holographic entanglement renormalisation of topological order in a quantum liquid

We introduce a novel momentum space entanglement renormalization group (MERG) scheme for the topologically ordered (T.O.) ground state of the 2D Hubbard model on a square lattice (\cite{anirbanmotti,anirbanmott2}) using a unitary quantum circuit comprised of non-local unitary gates. At each MERG step, the unitary quantum circuit disentangles a set of electronic states, thereby transforming the tensor network representation of the many-particle state. By representing the non-local unitary gate as a product of two-qubit disentangler gates, we provide an entanglement holographic mapping (EHM) representation for MERG. Using entanglement based measures from quantum information theory and complex network theory, we study the emergence of topological order in the bulk of the EHM. The MERG reveals distinct holographic entanglement features for the normal metallic, topologically ordered insulating quantum liquid and Neél antiferromagnetic symmetry-broken ground states of the 2D Hubbard model at half-filling found in Ref.\cite{anirbanmotti}. An MERG analysis of the quantum critical point of the hole-doped 2D Hubbard model found in Ref.\cite{anirbanmott2} reveals the evolution of the many-particle entanglement of the quantum liquid ground state with hole-doping, as well as how the collapse of Mottness is responsible for the emergence of d-wave superconductivity. We perform an information theoretic analysis of the EHM network, demonstrating that the information bottleneck principle is responsible for the distillation of entanglement features in the heirarchical structure of the EHM network. As a result, we construct a deep neural network (DNN) architecture based on our EHM network, and employ it for predicting the onset of topological order. We also demonstrate that the DNN is capable of distinguishing between the topologically ordered and gapless normal metallic phases.

cond-mat.str-el↗

arXiv2020

Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality

Capturing the interplay between electronic correlations and many-particle entanglement requires a unified framework for Hamiltonian and eigenbasis renormalization. In this work, we apply the unitary renormalization group (URG) scheme developed in a companion work (Ref.[1]) to the study of two archetypal models of stongly correlated lattice electrons, one with translation invariance and one without. We obtain detailed insight into the emergence of various gapless and gapped phases of quantum electronic matter by computing effective Hamiltonians as well as entanglement signatures through their respective tensor network descriptions. For the translationally invariant model of a single-band of interacting electrons, this includes results on gapless metallic phases such as the Fermi liquid and Marginal Fermi liquid, as well as gapped phases such as the reduced Bardeen-Cooper-Schrieffer, pair density-wave and Mott liquid phases. Additionally, a study of a generalised Sachdev-Ye model with disordered four-fermion interactions offers detailed results on many-body localised phases, as well as thermalised phase. We emphasise the distinctions between the various phases based on a combined analysis of their dynamical (obtained from the effective Hamiltonian) and entanglement properties. Importantly, the RG flow of the Hamiltonian vertex tensor network is shown to lead to emergent gauge theories for the gapped phases. Taken together with results on the holographic spacetime generated from the RG of the many-particle eigenstate (seen through, for instance, the holographic upper bound of the one-particle entanglement entropy), our analysis offer an ab-initio perspective of the gauge-gravity duality for quantum liquids that are emergent in systems of correlated electrons.

cond-mat.str-el↗

arXiv2020

Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach

We present a unified framework for the renormalisation of the Hamiltonian and eigenbasis of a system of correlated electrons, unveiling thereby the interplay between electronic correlations and many-particle entanglement. For this, we extend substantially the unitary renormalization group (URG) scheme introduced in Refs.\cite{anirbanmotti,anirbanmott2,mukherjee2020}. We recast the RG as a discrete flow of the Hamiltonian tensor network, i.e., the collection of various $2n$-point scattering vertex tensors comprising the Hamiltonian. The renormalisation progresses via unitary transformations that block diagonalizes the Hamiltonian iteratively via the disentanglement of single-particle eigenstates. This procedure incorporates naturally the role of quantum fluctuations. The RG flow equations possess a non-trivial structure, displaying a feedback mechanism through frequency-dependent dynamical self-energies and correlation energies. The interplay between various UV energy scales enables the coupled RG equations to flow towards a stable fixed point in the IR. The effective Hamiltonian at the IR fixed point generically has a reduced parameter space, as well as number of degrees of freedom, compared to the microscopic Hamiltonian. Importantly, the vertex tensor network is observed to govern the RG flow of the tensor network that denotes the coefficients of the many-particle eigenstates. The RG evolution of various many-particle entanglement features of the eigenbasis are, in turn, quantified through the coefficient tensor network. In this way, we show that the URG framework provides a microscopic understanding of holographic renormalisation: the RG flow of the vertex tensor network generates a eigenstate coefficient tensor network possessing a many-particle entanglement metric. We find that the eigenstate tensor network accommodates sign factors arising from fermion exchange.

cond-mat.str-el↗

arXiv2020

Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid

We perform a unitary renormalization group (URG) study of the 1D fermionic Hubbard model. The formalism generates a family of effective Hamiltonians and many-body eigenstates arranged holographically across the tensor network from UV to IR. The URG is realized as a quantum circuit, leading to the entanglement holographic mapping (EHM) tensor network description. A topological $Θ$-term of the projected Hilbert space of the degrees of freedom at the Fermi surface are shown to govern the nature of RG flow towards either the gapless Tomonaga-Luttinger liquid or gapped quantum liquid phases. This results in a nonperturbative version of the Berezenskii-Kosterlitz-Thouless (BKT) RG phase diagram, revealing a line of intermediate coupling stable fixed points, while the nature of RG flow around the critical point is identical to that obtained from the weak-coupling RG analysis. This coincides with a phase transition in the many-particle entanglement, as the entanglement entropy RG flow shows distinct features for the critical and gapped phases depending on the value of the topological $Θ$-term. We demonstrate the Ryu-Takyanagi entropy bound for the many-body eigenstates comprising the EHM network, concretizing the relation to the holographic duality principle. The scaling of the entropy bound also distinguishes the gapped and gapless phases, implying the generation of very different holographic spacetimes across the critical point. Finally, we treat the Fermi surface as a quantum impurity coupled to the high energy electronic states. A thought-experiment is devised in order to study entanglement entropy generated by isolating the impurity, and propose ways by which to measure it by studying the quantum noise and higher order cumulants of the full counting statistics.

cond-mat.str-el↗

arXiv2019

Scaling theory for Mott-Hubbard transitions

We present a $T=0K$ renormalization group (RG) phase diagram for the electronic Hubbard model in two dimensions on the square lattice at, and away from, half filling. The RG procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every RG step. The resulting phase diagram thus possess the quantum fluctuation energy scale ($ω$) as one of its axes. A relation is derived between $ω$ and the effective temperature scale upto which gapless, as well as emergent gapped, phases can be obtained. We find that the transition in the half-filled Hubbard model involves, for any on-site repulsion, passage from a marginal Fermi liquid to a topologically-ordered gapped Mott liquid through a pseudogapped phase bookended by Fermi surface topology-changing Lifshitz transitions. Using effective Hamiltonians and wavefunctions for the low-energy many-body eigenstates for the doped Mott liquid obtained from the stable fixed point of the RG flow, we demonstrate the collapse of the pseudogap for charge excitations (Mottness) at a quantum critical point possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-pseudogapping near the antinodes. d-wave Superconducting order is shown to arise from this quantum critical state of matter. Benchmarking of the ground state energy per particle and the double-occupancy fraction against existing numerical results also yields excellent agreement. We present detailed insight into the $T=0$ origin of several experimentally observed findings in the cuprates, including Homes law and Planckian dissipation. Our results offer insight on the ubiquitous origin of superconductivity in doped Mott insulating states, and pave the way towards a systematic search for higher superconducting transition temperatures in such systems.

cond-mat.str-el↗

arXiv2019

Non-perturbative approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets

We have formulated a twist operator argument for the geometrically frustrated quantum spin systems on the kagome and triangular lattices, thereby extending the application of the Lieb-Schultz-Mattis (LSM) and Oshikawa-Yamanaka-Affleck (OYA) theorems to these systems. The equivalent large gauge transformation for the geometrically frustrated lattice differs from that for non-frustrated systems due to the existence of multiple sublattices in the unit cell and non-orthogonal basis vectors. Our study for the $S=1/2$ kagome Heisenberg antiferromagnet at zero external magnetic field gives a criterion for the existence of a two-fold degenerate ground state with a finite excitation gap and fractionalized excitations. At finite field, we predict various plateaux at fractional magnetisation, in analogy with integer and fractional quantum Hall states of the primary sequence. These plateaux correspond to gapped quantum liquid ground states with a fixed number of singlets and spinons in the unit cell. A similar analysis for the triangular lattice predicts a single fractional magnetization plateau at $1/3$. Our results are in broad agreement with numerical and experimental studies.

cond-mat.str-el↗

arXiv2018

Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis

We analyse the antiferromagnetic spin-$1/2$ XXZ model on the kagome lattice at finite external magnetic field with the help of a nonperturbative zero-temperature renormalization group (RG) technique. Following the work of Kumar \emph{et al} (Phys. Rev. B {\bf 90}, 174409 (2014)), we use a Jordan-Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbour interactions. While the work of Kumar \emph{et al} was confined mostly to the plateau at $1/3$-filling (magnetisation per site) in the XY regime, we analyse the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel-Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a $SU(2)$-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar \emph{et al}. We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.

cond-mat.str-el↗

arXiv2016

Classical Electrodynamics in a Unified Theory

Some consequences of a fully classical unified theory of gravity and electromagnetism are worked out for the electromagnetic sector such as the occurrence of classical light beams with spin and orbital angular momenta that are topologically quantized in units of $q_e q_m=σ$, independent of the beam size. Empirical fits require $σ= \hbar$. The theory also predicts a generalized coherency matrix whose consequences are testable.

physics.optics↗

arXiv2014

Intensity-Intensity Correlations of Classically Entangled Light

An experiment is proposed to show that after initial frequency and polarization selection, classical thermal light from two independent sources can be made path-polarization entangled. Such light will show new intensity-intensity correlations involving both path and polarization phases, formally similar to those for four-particle GHZ states. For fixed polarization phases, the correlations reduce to the Hanbury Brown-Twiss phase correlations. It is also shown that these classical correlations violate noncontextuality.

quant-ph↗

arXiv2013

Novel States of Classical Light and Noncontextuality

A new criterion, based on noncontextuality, is derived to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. An experiment is proposed to test the violation of noncontextuality by a nonseparable state. Such states have only recently begun to be explored. The significance of their nonseparability or entanglement as well as their similarities with and differences from entangled quantum states are discussed.

quant-ph↗

arXiv2013

Entanglement in Classical Optics

The emerging field of entanglement or nonseparability in classical optics is reviewed, and its similarities with and differences from quantum entanglement clearly pointed out through a recapitulation of Hilbert spaces in general, the special restrictions on Hilbert spaces imposed in quantum mechanics and the role of Hilbert spaces in classical polarization optics. The production of Bell-like states in classical polarization optics is discussed, and new theorems are proved to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. The influence of the Pancharatnam phase on a classical Bell-like state is deived. Finally, to what extent classical polarization optics can be used to simulate quantum information processing tasks is also discussed. This should be of great practical importance because coherence and entanglement are robust in classical optics but not in quantum systems.

physics.optics↗