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Numerical variational technique
The density matrix renormalization group (DMRG) is a numerical variational technique devised to obtain the low-energy physics of quantum many-body systems
Density matrix renormalization group
Density_matrix_renormalization_group
Graph representation in quantum mechanics
entanglement renormalization ansatz (MERA). Tensor networks provide the theoretical and computational framework underlying the density matrix renormalization group
Tensor_network
Concept in theoretical physics
In theoretical physics, the renormalization group (RG) is a mathematical tool that allows systematic investigation into the changes in a physical system
Renormalization_group
Quantum state of multiple particles represented as complex matrices
A matrix product state (MPS) is a representation of a quantum many-body state. It is at the core of the density matrix renormalization group (DMRG) algorithm
Matrix_product_state
Theoretical chemist
quantum many-body systems in chemistry and physics, including density matrix renormalization group (DMRG) theory and tensor network algorithms. Chan attended
Garnet_K.-L._Chan
Topics referred to by the same term
block device, as in the Unix File System Superblock, in the density matrix renormalization group numerical technique Superblock algorithm, in the pairwise
Superblock
American physicist
quantum spin liquids. He is most known for inventing the Density Matrix Renormalization Group (DMRG) in 1992. This is a numerical variational technique
Steven_R._White
Theoretical framework in physics
Costello's monograph Renormalization and Effective Field Theory provides a rigorous formulation of perturbative renormalization that combines both the
Quantum_field_theory
Spanish theoretical physicist, author, and academic
G. (1998). Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains. Europhysics letters
Germán_Sierra
Approximating method in quantum mechanics
bound to the ground state energy. The Hartree–Fock method, density matrix renormalization group, and Ritz method apply the variational method. Suppose we
Variational method (quantum mechanics)
Variational_method_(quantum_mechanics)
Concept in quantum physics
reduces the complexity of quantum many-body systems. The density matrix renormalization group and matrix product states, for example, implicitly rely on such
Entropy_of_entanglement
Tiling of a plane by regular hexagons and equilateral triangles
quantum spin liquid ground state without magnetic order. Density matrix renormalization group calculations point to a gapped spin liquid, and inelastic
Trihexagonal_tiling
Classification of molecular orbitals used in multireference quantum chemistry
procedure based on orbital-entanglement measures obtained from density-matrix renormalization group calculations. Related open-source software includes the Active
Complete_active_space
Model in topological quantum mechanics
S2CID 55330505. Schollwöck, Ulrich (2011). "The density-matrix renormalization group in the age of matrix product states". Annals of Physics. 326 (1): 96–192
AKLT_model
Lowest possible energy of a quantum system or field
theory led to the idea of incorporating renormalization into QED to deal with zero-point infinities. Renormalization was originally developed by Hans Kramers
Zero-point_energy
Probabilistic algorithms to simulate quantum many-body systems
Carlo method QMC@Home Quantum chemistry Quantum Markov chain Density matrix renormalization group Time-evolving block decimation Metropolis–Hastings algorithm
Quantum_Monte_Carlo
Class of quantum field theory models
Nevertheless, they exhibit a non-trivial ultraviolet fixed point of the renormalization group both in the lattice formulation and in the double expansion originally
Non-linear_sigma_model
Singularities in the parameter space
higher-order. Many numerical methods such as the Lanczos algorithm, Density Matrix Renormalization Group (DMRG), and other tensor network algorithms are relatively
Exceptional_point
PCP theorem is an open problem. Hamiltonian simulation Density matrix renormalization group Matrix product state Osborne, Tobias J. (2011). "Hamiltonian
Hamiltonian_complexity
Argentine physicist (born 1964)
Hallberg worked on several numerical tools, including the density matrix renormalization group (DMRG), a numerical method that can be used for low-dimensional
Karen_Hallberg
Hartree–Fock method, 1964 density functional theory and variational Monte Carlo and 1992 density matrix renormalization group (DMRG).[citation needed]
History of variational principles in physics
History_of_variational_principles_in_physics
Theory of the strong nuclear interactions
mass and coupling of the theory, respectively, which are subject to renormalization. An important theoretical concept is the Wilson loop (named after Kenneth
Quantum_chromodynamics
Belgian quantum physicist (born 1972)
for the density matrix renormalization group. They extended the framework to finite temperature and dissipation through matrix product density operators
Frank_Verstraete
Quantum field theory of electromagnetism
though renormalization works well in practice, Feynman was never entirely comfortable with its mathematical validity, referring to renormalization as a
Quantum_electrodynamics
Problem in physics and quantum mechanics
approaches Density functional theory Lattice gauge theory Matrix product state Neural network quantum states Numerical renormalization group Jenkins, Stephen
Many-body_problem
Model of interacting spinless bosons on a lattice
[citation needed] One-dimensional lattices may be studied using density matrix renormalization group (DMRG) and related techniques such as time-evolving block
Bose–Hubbard_model
Formulation of quantum mechanics
Changing the scale of the regulator leads to the renormalization group. In fact, renormalization is the major obstruction to making path integrals well-defined
Path-integral_formulation
Quantum many-body simulation algorithm
exponential scaling, including quantum Monte Carlo and the density matrix renormalization group. Guifré Vidal proposed the scheme while at the Institute
Time-evolving block decimation
Time-evolving_block_decimation
Physical theory with fields invariant under the action of local "gauge" Lie groups
of some computations: for example Ward identities connect different renormalization constants. The first gauge theory quantized was quantum electrodynamics
Gauge_theory
Quantum chromodynamics on a lattice
(such as the scattering matrix) are expanded in powers of the lattice spacing, a. The results are used primarily to renormalize Lattice QCD Monte-Carlo
Lattice_QCD
Argentinian-American theoretical physicist
computational techniques is crucial. He has employed Monte Carlo, density matrix renormalization group, and Lanczos methods. Together with collaborators, he also
Elbio_Dagotto
Technique in computational quantum field theory
off-diagonal matrix elements and gauge projections. Physical quantities can then be computed from the right and left LFCC eigenstates. Renormalization concepts
Light-front computational methods
Light-front_computational_methods
Force resulting from the quantisation of a field
quantum field theorists before the development in the 1970s of the renormalization group, a mathematical formalism for scale transformations that provides
Casimir_effect
Basic result in harmonic analysis on compact topological groups
Moreover, the matrix coefficients of the irreducible unitary representations form an orthonormal basis of L2(G). In the case that G is the group of unit complex
Peter–Weyl_theorem
Procedure of coping with redundant degrees of freedom in physical field theories
application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically
Gauge_fixing
Mathematical approach to quantum physics
of the other energy eigenstates k ≠ n. Each term is proportional to the matrix element ⟨ k ( 0 ) | V | n ( 0 ) ⟩ {\displaystyle \langle k^{(0)}|V|n^{(0)}\rangle
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Annual award by the National Academy of Sciences
physics, particularly for his development of density matrix renormalization group methods and the density matrix embedding theory. Theodore Betley (2013,
William O. Baker Award for Initiatives in Research
William_O._Baker_Award_for_Initiatives_in_Research
Relativistic wave equation describing massless fermions
_{y}&\sigma _{z}\end{pmatrix}}} is a vector whose components are the 2×2 identity matrix I 2 {\displaystyle I_{2}} for μ = 0 {\displaystyle \mu =0} and the Pauli
Weyl_equation
Theorem for reducing high-order derivatives
theory a different type of expectation value, a thermal trace over the density matrix, requires a different definition of normal ordering. Isserlis' theorem
Wick's_theorem
British theoretical physicist and mathematician (1923–2020)
theory and developed rules for the diagrams that completely solved the renormalization problem. Dyson's paper and his lectures presented Feynman's theories
Freeman_Dyson
Method used in mathematical physics
usually followed by a related, but independent technique called renormalization. Renormalization is based on the requirement that some physical quantities —
Regularization_(physics)
Taiwanese-American condensed matter physicist
signatures. Two years later, his group explored the extended spin-1/2 honeycomb XY model using density matrix renormalization group theory, revealing the emergence
Chin-Sen_Ting
Pictorial representation of the behavior of subatomic particles
procedure, to include particle self-interactions. The technique of renormalization, suggested by Ernst Stueckelberg and Hans Bethe and implemented by
Feynman_diagram
Mathematical structures that allow quantum mechanics to be explained
quantum state of the composite system is called a separable state. The density matrix of a bipartite system in a separable state can be expressed as ρ = ∑
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
describing the change of coupling constant under the renormalization group flow γ 1. Dirac matrix 2. One of the two conformal superghost fields β, γ
Glossary_of_string_theory
Formulation to quantize gauge field theories in physics
to say that the quantization and renormalization prescriptions were as much part of the model as the Lagrangian density, especially when they relied on
BRST_quantization
Second-rank tensor in quantum chromodynamics
components, that in a fixed gauge are 3×3 traceless Hermitian matrix-valued functions, while A μ a {\displaystyle {\mathcal {A}}_{\mu }^{a}}
Gluon_field_strength_tensor
Densitometry Density Density functional theory Density matrix Density matrix renormalization group Density of air Density of states Density wave theory
Index_of_physics_articles_(D)
Croatian theoretical physicist
necessarily have negative energy density values. Together with Henri Epstein, he found a new approach to renormalization theory called causal perturbation
Vladimir_Jurko_Glaser
Wave equations respecting special and general relativity
mathematical form of a wave equation or are generated from a Lagrangian density and the field-theoretic Euler–Lagrange equations (see classical field theory
Relativistic_wave_equations
Theory of subatomic structure
however, is not only algebraic: it can modify the flow of the renormalization group of the theory. Orientifolds Ω {\displaystyle \Omega } can be classified
String_theory
Equations for correlation functions in QFT
functions vanish.) Functional renormalization group Dyson equation Path integral formulation Source field F. Dyson (1949). "The S Matrix in Quantum Electrodynamics"
Schwinger–Dyson_equation
Soviet theoretical physicist (1908–1968)
physicist. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum
Lev_Landau
Collection of random variables
– via Google Books. Latouche, G.; Ramaswami, V. (1999). Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM. ISBN 978-0-89871-425-8 –
Stochastic_process
Energy difference between ground state and lightest excited state(s)
Tamhankar, S.; Young, B. L.; Zhang, J. B. (2006). "Glueball Spectrum and Matrix Elements on Anisotropic Lattices". Physical Review D. 73 (1) 014516. arXiv:hep-lat/0510074
Mass_gap
Branch of physics
unified by Kenneth G. Wilson in 1972, under the formalism of the renormalization group in the context of quantum field theory. The quantum Hall effect
Condensed_matter_physics
Symmetry between bosons and fermions
gauge couplings fail to unify at high energy. In particular, the renormalization group evolution of the three gauge coupling constants of the Standard
Supersymmetry
Formulation of classical mechanics
density is also the kinetic energy density of the field, minus its potential energy density (this is not true in general, and the Lagrangian density has
Lagrangian_mechanics
Physical quantities taking values at each point in space and time
anisotropic diffusion, which are framed as matrix-tensor PDEs, and then require matrices or tensor fields, hence matrix or tensor calculus. The scalars (and
Field_(physics)
Technique in computational quantum field theory
both cases the success of the renormalization program requires that the theory has a fixed point of the renormalization group; however, the details of the
Light_front_quantization
Hypothetical elementary particle that mediates gravity
field theory of gravitons due to the unsolved mathematical problem of renormalization in general relativity. This problem is avoided in string theory, which
Graviton
Wave equation for arbitrary spin particles
(1997). "Wigner Representation Theory of the Poincaré Group, Localization, Statistics and the S-Matrix". Nuclear Physics B. 499 (3): 519–546. arXiv:hep-th/9608092
Bargmann–Wigner_equations
Mathematics of a particle physics model
precisely, the renormalization scale used to calculate this energy) may also be treated as an additional free parameter. The renormalization scale may be
Mathematical formulation of the Standard Model
Mathematical_formulation_of_the_Standard_Model
French physicist (born 1938)
statistical physics. It uses the theoretical formulation of the renormalization group for critical phenomena (equation of states, scaling corrections
Édouard_Brézin
Dissipation in quantum systems
is of Kosterlitz–Thouless kind, as can be seen by deriving the renormalization group flow equations for the hopping term. A different approach to describe
Quantum_dissipation
Setting of relativistic physics in geometric algebra
generated by the Dirac matrices over the field of real numbers; explicit matrix representation is unnecessary for STA. Products of the basis vectors generate
Spacetime_algebra
Mathematical model of ferromagnetism in statistical mechanics
critical point can be described by a renormalization group fixed point of the Wilson-Kadanoff renormalization group transformation. It is also believed
Ising_model
Physical process of transition between basic states of matter
explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as γ {\displaystyle
Phase_transition
Algebra of 4D spacetime
L=e^{W/2}.} In the matrix representation, the Lorentz rotor is seen to form an instance of the SL(2, C) group (special linear group of degree 2 over the
Algebra_of_physical_space
Quantum mechanics taking into account particles near or at the speed of light
coining the term "quantum electrodynamics". 1943 Tomonaga begins work on renormalization, influential in QED. 1947 Schwinger calculates the anomalous magnetic
Relativistic quantum mechanics
Relativistic_quantum_mechanics
Relativistic interaction in quantum physics
electronic structure are obtained by diagonalization of the (2J + 1)-dimensional matrix. The fine electronic structure can be directly detected by many different
Spin–orbit_interaction
Statistical model used in machine learning
{\frac {df_{1}^{-1}(z_{1})}{dz_{1}}}} is the determinant of the Jacobian matrix of f 1 − 1 {\displaystyle f_{1}^{-1}} . By the inverse function theorem:
Flow-based_generative_model
Type of topological defects in the Yang–Mills vacuum
, {\displaystyle z_{n}=e^{\frac {2\pi in}{N}}I\;,} where I is the unit matrix. These elements form the abelian subgroup ZN. Under such center elements
Center_vortex
Mechanism that explains the generation of mass for gauge bosons
16 June 2012. 't Hooft, G.; Veltman, M. (1972). "Regularization and renormalization of gauge fields". Nuclear Physics B. 44 (1): 189–219. Bibcode:1972NuPhB
Higgs_mechanism
Superconductivity theory
with Brian Greene they argued that these theories are related by a renormalization group flow to sigma models on Calabi–Yau manifolds. In his 1993 paper
Ginzburg–Landau_theory
Nonlinear partial differential equation
Kosterlitz–Thouless transition for vortices can therefore be derived from a renormalization group analysis of the sine-Gordon field theory. The sine-Gordon equation
Sine-Gordon_equation
Ensemble of states with an exactly specified total energy
ISBN 978-0-486-65242-9. Nigel Goldenfeld; Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics 85, Westview Press (June, 1992) ISBN 0-201-55409-7
Microcanonical_ensemble
Extension of quantum field theory to curved spacetime
the viewpoint of local quantum physics is suitable to generalize the renormalization procedure to the theory of quantum fields developed on curved backgrounds
Quantum field theory in curved spacetime
Quantum_field_theory_in_curved_spacetime
Mathematical transform that expresses a function of time as a function of frequency
a density function, and one must treat not functions but distributions, i.e., measures that possess "atoms". From the higher point of view of group characters
Fourier_transform
Model of hadrons
particles, parton densities cannot be calculated using perturbative QCD. Within QCD one can, however, study variation of parton density with resolution
Parton_(particle_physics)
Chinese-American physicist (1926–2024)
and other instanton problems. They also did work on the neutrino mapping matrix. Lee was one of the 20 American recipients of the Nobel Prize in Physics
Tsung-Dao_Lee
Generalization of electrodynamics
higher-order charges are often divergent before renormalization. To make them finite, symplectic renormalization is used, which exploits the ambiguities of
P-form_electrodynamics
Properties underlying modern physics
representation Renormalization group Representation of a Lie group Representation theory of the Lorentz group Representation theory of the Poincaré group Spin-statistics
Symmetry_in_quantum_mechanics
Partial differential equation
H. K. (1976). "On a Lagrangean for Classical Field Dynamics and Renormalization Group Calculation of Dynamical Critical Properties". Z. Phys. B23 (4):
Fokker–Planck_equation
Mechanism recovering classical behavior from a quantum system
coherence of a sample is explained by the off-diagonal elements of a density matrix. An external electric or magnetic field can create coherences between
Dephasing
Network whose degree distribution follows a power law
{\displaystyle k\to k+\epsilon k} , evoking parallels with the renormalization group techniques in statistical field theory. However, there's a key difference
Scale-free_network
Result of repeatedly applying a mathematical function
computer science, fractals, dynamical systems, mathematics and renormalization group physics. The formal definition of an iterated function on a set
Iterated_function
Renormalizable Renormalization Renormalization group Renormalon Replica trick Reports on Progress in Physics Representation theory of the Galilean group Representation
Index_of_physics_articles_(R)
American mathematician (born 1937)
[math-ph]. Balaban, Tadeusz; Imbrie, John; Jaffe, Arthur (1985), "Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean
Arthur_Jaffe
British physicist (1902–1984)
equations so that they involved directly observable quantities, leading to the matrix formulation of quantum mechanics. Fowler sent Heisenberg's paper on to Dirac
Paul_Dirac
Non-mathematical introduction
later, renormalization largely solved this problem. Initially viewed as a provisional, suspect procedure by some of its originators, renormalization eventually
Introduction to quantum mechanics
Introduction_to_quantum_mechanics
Theories trying to extend known physics
U(1) symmetry, corresponding to the three fundamental forces. Due to renormalization the coupling constants of each of these symmetries vary with the energy
Physics beyond the Standard Model
Physics_beyond_the_Standard_Model
Applications of machine learning to quantum physics
PMID 30552316. Bény, Cédric (2013-01-14). "Deep learning and the renormalization group". arXiv:1301.3124 [quant-ph]. Arunachalam, Srinivasan; de Wolf,
Machine_learning_in_physics
Russian physicist and mathematician
Korepin evaluated the entanglement entropy and studied the reduced density matrix. He also worked on quantum search algorithms with Lov Grover. Many of
Vladimir_Korepin
Interdisciplinary research area
PMID 30552316. Bény, Cédric (2013-01-14). "Deep learning and the renormalization group". arXiv:1301.3124 [quant-ph]. Arunachalam, Srinivasan; de Wolf,
Quantum_machine_learning
Elementary particle or quantum of light
Such unphysical results are corrected for using the technique of renormalization. Other virtual particles may contribute to the summation as well; for
Photon
Theory of forces and subatomic particles
U=e^{-ig_{\text{s}}\lambda ^{a}\phi ^{a}(x)}} is 3 × 3 unitary matrix with determinant 1, making it a member of the group SU(3), and ϕ a ( x ) {\displaystyle \phi ^{a}(x)}
Standard_Model
Functional relationship between two quantities
scaling behaviour as they approach criticality—can be shown, via renormalization group theory, to share the same fundamental dynamics. For instance, the
Power_law
Feature detection algorithm in computer vision
each element is computed, followed by ℓ 2 {\displaystyle \ell ^{2}} -renormalization. After these algebraic manipulations, RootSIFT descriptors can be normally
Scale-invariant feature transform
Scale-invariant_feature_transform
Mathematical model of the time dependence of a point in space
ensemble averages and this links it deeply with Ergodic theory and the Renormalization group. Key aspect of effective dynamics is the concept of emergence, such
Dynamical_system
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DENSITY MATRIX-RENORMALIZATION-GROUP
DENSITY MATRIX-RENORMALIZATION-GROUP
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Male
French
French and German form of Greek Mattathias, MATHIS means "gift of God."
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Male
Italian
Italian form of Hebrew Mattithyah, MATTIA means "gift of God."
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
Male
Hungarian
Czech and Hungarian form of Greek Patrikios, PATRIK means "patrician, of noble descent."
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Female
German
Pet form of German Katarine, KATRIN means "pure."
Female
Finnish
Pet form of Finnish Katariina, KATRI means "pure."
Girl/Female
Maori
The Maori form of April.
Girl/Female
Biblical
Rain, prison.
Male
English
Anglicized form of Irish Gaelic MainchÃn, MANNIX means "little monk."
Surname or Lastname
English (of Welsh origin)
English (of Welsh origin) : variant of Maddox.
Female
English
French form of Latin Maria, MARIE means "obstinacy, rebelliousness" or "their rebellion."
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
DENSITY MATRIX-RENORMALIZATION-GROUP
DENSITY MATRIX-RENORMALIZATION-GROUP
DENSITY MATRIX-RENORMALIZATION-GROUP
DENSITY MATRIX-RENORMALIZATION-GROUP
DENSITY MATRIX-RENORMALIZATION-GROUP
DENSITY MATRIX-RENORMALIZATION-GROUP
DENSITY MATRIX-RENORMALIZATION-GROUP
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