Condensed matter theory journal clubHelp

Abstract: "We will start by reviewing, following [1], the main known results for area laws of entanglement entropy in ground states of quantum many-body systems in both 1D and higher dimensions. We will highlight the connections between these results and the possibility of efficiently simulate interacting systems. We will then focus on out-of-equilibrium settings and in particular prove, following [2][3][4], that systems evolving according to local finite-dimensional Hamiltonians still satisfy, for finite times, an area law for the entanglement entropy."
[1] Eisert, Cramer, Plenio - Colloquium: Area laws for the entanglement entropy
[2] Bravyi, Hastings, Vestraete - Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order
[3] Dur, Vidal, Cirac, Linden, Popescu - Entanglement Capabilities of Nonlocal Hamiltonians
[4] Childs, Leung, Vidal - Reversible simulation of bipartite product Hamiltonians

Abstract: "Macroscopic fluctuation theory (MFT) is a large deviation theory that allows us to study important dynamical properties, such as current fluctuations, of the diffusive many-body system based on hydrodynamics. In this talk I will illustrate the basic idea of MFT by applying it to compute the total current cumulant generating function. I will also briefly touch upon the recent development on the exact solution of MFT for the symmetric simple exclusion process."
[1] B. Derrida - J. Stat. Mech. (2007) P07023.
[2] L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim - Rev. Mod. Phys. 87, 593 (2015).
[3] P. L. Krapivsky, K. Mallick, and T. Sadhu - J. Stat. Phys. 160, 885 (2015).
[4] K. Mallick, H. Moriya, and T. Sasamoto - Phys. Rev. Lett. 129, 040601 (2022).

Abstract: In this paper [1], the authors introduce a random-interaction all-to-all fermionic model, which they dub the “Wishart-Sachdev-Ye-Kitaev” (WSYK) model. The model possesses large degeneracies in its spectrum which grow exponentially with increasing system size. The authors proceed to demonstrate that this model is a particular case of the Richardson-Gaudin model, and is hence integrable. In my talk, I will review the main results and derivations of the paper and contrast the integrable WSYK model with the original chaotic SYK model of which it is a variant. In the process, I will introduce a number of concepts relevant to contemporary research in condensed matter physics, such as level statistics and quantum integrability.
[1] Eiki Iyoda et al. - Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models

Abstract: I will review a construction [1] to produce wave functions invariant under symmetry. A common mechanism to restore symmetry is by condensing symmetry-breaking domains starting from an ordered state. This typically produces a trivial symmetry unbroken paramagnetic product state. If, however, the domain walls are bound to lower-dimensional symmetric wavefunctions, this condensate can produce more exotic wavefunctions, eg: which can host gapless surface states. I will demonstrate this using simple examples and state some general pictures.
[1] Xie Chen et al. - Symmetry-protected topological phases from decorated domain walls

Abstract: In this paper, Senthil examined a possible scenario where non-Fermi liquids occurred. By tuning Fermi surfaces to criticality, he showed that the scaling ansatz of the spectral functions lead to consequences that are in accordance with certain phenomena observed in the normal states of cuprates. In this journal club talk, I will walk through the hypotheses and the arguments made in the paper, and if time permits, I will present a mean field slave particle calculation in the paper, which provides some evidences for the notion of critical Fermi surface.
T. Senthil. - Critical fermi surfaces and non-fermi liquid metals

Abstract: I will review two papers which present a graph theoretic characterisation of when spin ½ Hamiltonians can be represented in terms of free fermions. I will primarily focus on [1] in which the authors focus on mappings between elements of the Pauli algebra spanned by the terms in the Hamiltonian and fermionic bilinears, which thus form generalized Jordan-Wigner mappings. The authors show that mappings of this kind are possible if and only if the associated frustration graph of the Hamiltonian is the line graph of a reference graph R, which is to be thought of as describing the hoppings of the fermions. I will discuss some examples of this construction. If time permits I will turn to the newer results in [2] which show that relaxing the conditions in [1] we can capture examples where the map to fermions depends upon the coupling strengths and moreover that if the frustration graph has the weaker property of containing no 'claw' subgraphs, that the original spin model is integrable.
[1] S.J. Elman et al. - Characterization of solvable spin models via graph invariants
[2] S.J. Elman et al. - Free fermions behind the disguise

Abstract: In this paper [1] Lensky and collaborators offer a theoretical supplement to a recent experimental study [2] done on the Google’s sycamore chip where the main results was the observation of the non-Abelian anyon braiding statistics in the Toric code with lattice dislocations. This paper presents a substantial elaboration on the original proposal made by Bombin in his 2010 paper [3] along side a physically motivated reinterpretation.
[1] Yuri Lensky et al. - Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code
[2] Google Quantum AI - Observation of non-Abelian exchange statistics on a superconducting processor
[3] H. Bombin - Topological order with a twist: Ising anyons from an abelian model

Abstract: In this paper [1], Schulz introduces a new method to analyse the Hubbard Model that manages to reproduce both the correct Hartree-Fock saddle point, and the massless fluctuations around it. This method is then used to study the problem of a nearly half filled Hubbard model, recovering results that were previously introduced via semi-phenomenological arguments by Shankar[2]. In the talk I will also mention the potential uses of a generalization of this method in a broader context.
[1] H.J. Schultz - Effective action for strongly correlated fermions from functional integrals
[2] R. Shankar - Holes in a quantum antiferromagnet: New approach and exact results

Cellular automata and their applications in studying topological phases of matter, or "Something non-trivial in dimension three."
Jeongwan Haah, Clifford Quantum Cellular Automata:Trivial group in 2D and Witt group in 3D
Jeongwan Haah, Commuting Pauli Hamiltonians as Maps between Free Modules
Jeongwan Haah, Lukasz Fidkowski, and Matthew B. Hastings, Nontrivial Quantum Cellular Automata in Higher Dimension

"Continuum Model of Twisted Bilayer Graphene"

Rafi Bistritzer and Allan H. MacDonald, "Moiré bands in twisted double-layer graphene" -- https://www.pnas.org/content/108/30/12233

Grigory Tarnopolsky, Alex Jura Kruchkov, and Ashvin Vishwanath, "Origin of Magic Angles in Twisted Bilayer Graphene" -- https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.106405

Hoi Chun Po, Liujun Zou, Ashvin Vishwanath, and T. Senthil, "Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene" -- https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.031089

Key ideas of modern real-space renormalization methods.
S. White, Density-matrix formulation of quantum renormalization groups
G. Vidal, Entanglement renormalization
M. Levin and C. Nave, Tensor Renormalization Group Approach to Two-Dimensional Classical Lattice Models
G. Evenbly and G. Vidal, Tensor network renormalization

A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig (2008), "Classification of topological insulators and superconductors in three spatial dimensions"
A. Kitaev (2009), "Periodic table for topological insulators and superconductors"
A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig (2009), "Classification of Topological Insulators and Superconductors"
M. Nakahara (2003), "Geometry, Topology and Physics"

L.S. Levitov (1988), "Why Only Quadratic Irrationalities Are Observed in Quasicrystals?"

Thouless, Kohmoto, Nightingale, and den Nijs (1982), "Quantized Hall Conductance in a Two-Dimensional Periodic Potential"

W. Kohn and J. M. Luttinger, PRL 15, 12, 1965, "New Mechanism for Superconductivity",
J. M. Luttinger, Phys. Rev. 150, 1, 1966, "New Mechanism for Superconductivity".

G. Lindblad, Comm. Math. Phys. 48 (1976), 119-130, "On the generators of quantum dynamical semigroups",
V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. of Math. Phys. 17, 821 (1976), "Completely positive dynamical semigroups of N-level systems",
T. Prosen, New Journal of Physics 10 (2008) 043026, "Third quantization: a general method to solve master equations for quadratic open Fermi systems".

1. Original paper: Phys Rev 119 4. J.M.Luttinger. (1960) ,
   


2. Two papers on non-perturbative approaches:
• 1D: PRL 78 10 M.Oshikawa et al. (1996)
• 2D: PRL 84 15 M.Oshikawa. (1999)
3. Luttinger theorem according to the notion of Luttinger surface: PRB 68 085113 I.Dzyaloshinskii (2003) ,


4. Relation between the Luttinger theorem and the zeros of the single particle Green function: PRL 110, 090403 K.B. Dave, P.W.Phillips and C.L. Kane (2013).


5. And some of its applications in strongly correlated systems.

1. Kenyon (2002), The Laplacian and Dirac operators on critical planar graphs ,


2. Mercat (2009), Discrete Riemann surfaces and the Ising model ,


3. Chelkak and Smirnov (2012), Universality in the 2D Ising model and conformal invariance of fermionic observables .

Useful references to learn about the subject:
https://arxiv.org/abs/0910.1130,
https://arxiv.org/abs/1308.3318,
https://arxiv.org/abs/1306.2164.
For parent Hamiltonians and the topological classification using tensor networks (more advanced), see
https://arxiv.org/abs/quant-ph/0608197,
https://arxiv.org/abs/0901.2223,
https://arxiv.org/abs/1010.3732,
https://arxiv.org/abs/1001.3807.

[1] N. Temperley, E. Lieb, Proceedings of the Royal Society Series A 322 (1971), 251-280.
[2] Integrable lattice models and quantum groups. H. Saleur, J.B. Zuber (1990), Lectures given at Conference: C90-04-23 (Trieste Spring School 1990:0001-54).
[3] Logarithmic Conformal Field Theory: a Lattice Approach. A.M. Gainutdinov, J.L. Jacobsen, N. Read, H. Saleur, R. Vasseur, J. Phys. A: Math. Theor. 46 (2013) 494012

"Quantum Computation and Quantum Information" by Niesel and Chuang

Sidney Coleman (1975), Quantum sine-Gordon equation as the massive Thirring model

Levitov, Shytov, and Yakovets, Phys. Rev. Lett. 75, 370 (1995)

(1) Main reference: G. Vidal, “Classical simulation of infinite-size quantum lattice systems in one spatial dimension”, Phys. Rev. Lett. 98, 070201 (2007) or on Arxiv,
(2) If time allows it: R. Orús and G. Vidal, “Infinite time-evolving block decimation algorithm beyond unitary evolution”, Phys. Rev. B 78, 155117 (2008),
(3) Technical review of MPS and MPO: U. Schollwoeck, “The density-matrix renormalization group in the age of matrix product states”, Annals of Physics 326, 96 (2011),
(4) Non-technical introduction to MPS and MPO: R. Orús, “A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States”, Annals of Physics 349 (2014) 117-158.

Cats can land on their feet when they are held upside down and released from rest. Divers can perform multiple twists before hitting the water. In both cases, a deformable body with zero total angular momentum rotates itself by executing a sequence of deformations. Following Shapere and Wilczek [1], I will show that the kinematics of reorientation is naturally understood in terms of non-Abelian Berry phase in the space of shapes. As an application of their theory, I analyze the falling cat problem following Montgomery's treatment [2]. I will demonstrate that the shape space of Kane-Scher cat (a simplistic model of cat kinematics) is homeomorphic to the real projective plane and its self-rotation sequence maps to a non-contractible loop that picks up a pi flux.
[1] Alfred Shapere and Frank Wilczek ``Gauge Kinematics of Deformable Bodies'' in Geometric Phases in Physics, World Scientific, 1989.
[2] Richard Montgomery ``Gauge Theory of the Falling Cat'', Fields Institute Communications 1, 193 (1993).
Journal Club notes by Yuan himself.

On the one hand, there has been a recent surge of interest in periodically driven (“Floquet”) systems, in particular how they can realize phases and excitations not found in equilibrium. On the other, conformal field theory (CFT), which describes a broad class of quantum critical points with emergent conformal symmetry, has become a pillar of condensed matter physics in the last few decades. Given their naturalness in studying so-called “quantum quenches” and other non-equilibrium phenomena, CFTs have proven to be a useful playground for studying non-equilibrium dynamics. We will give a lightning introduction to both CFTs and to Floquet systems, ending with an overview of our recent work on CFTs subject to a periodic boundary drive.
W. Berdanier, M. Kolodrubetz, R. Vasseur, and J. E. Moore. ``Floquet Dynamics of Boundary-Driven Systems at Criticality.'' Phys. Rev. Lett. 118, 260602 (2017)

(1) L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, “From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics”, Advances in Physics Vol. 65, No. 3, 239-362 (2016) or on Arxiv,
(2) M. Srednicki, “Chaos and Quantum Thermalization”, Phys. Rev. E 50, 888 (1994) ,
(3) J.M. Deutsch, “Quantum statistical mechanics in a closed system”, Phys. Rev. A 43, 2046 (1991).

Topologically ordered phases in two dimensions can be used as quantum memories that are insensitive to local errors. but are not protected from thermal errors due to the tendency of local excitations to spatially separate. Haah's cubic code is a 3D topologically ordered Hamiltonian where local excitations cannot be separated without paying a large energy cost, and so gains an enhanced robustness to thermal errors. In this talk, I will introduce the stabilizer code formalism that allowed for this Hamiltonian to be found, discuss the "fractal-like" structure of excitations in Haah's code, and discuss the thermal protection that results.
(1) Haah Local stabilizer codes in three dimensions without string logical operators (2011)
(2) Prem, Haah, Nandkishore Glassy quantum dynamics in translation invariant fracton models (2017)

I'll look at deriving the linearised structure of quantum Hall edges in a few ways, each of which has its own merits. (1) I'll begin with Wen's hydrodynamics approach before (2) moving on to a more rigorous microscopic derivation of the edge structure. If time permits I'll also discuss (3) the description in terms of Chern-Simons theories. (NB: Given the limited preparation time this may be subject to last-minute changes)
(1) Xiao-Gang's paper and Chang's paper in Geometric Phases in Physics, World Scientific, 1989.
(2) Macdonald's notes, among others.
(3) David Tong's lecture notes.

I will review the main aspects of the many-body localisation transition and analyse some well-understood quantities, useful to quantitatively distinguish MBL from ETH. Recently the athermality of the MBL phase has been proposed as an important feature with possible thermodynamic applications. In particular, I will show how the different spectral statistics between MBL and ETH can be used to devise a quantum version of the thermodynamic Otto cycle. In this case, a many-body quantum system is cyclically ramped from the localised to the ergodic phase extracting work after each period. MBL can then be used to enhance the overall efficiency of the protocol.
(1) Many-body localization: an introduction and selected topics, https://arxiv.org/abs/1711.03145.
(2) MBL-mobile: Many-body-localized engine https://arxiv.org/abs/1707.07008.

Lecture notes by M. Hastings, arXiv:1008.5137
M. Hastings, arXiv:1008.5137
M. B. Hastings, X.-G. Wen Phys. Rev. B 72 045141 (2005)
E. H. Lieb, D. W. Robinson, Commun. math. Phys. 28, 251-257 (1972)
Application arXiv:1506.03455

B. L. Altshuler, B. I. Shklovskii, Zh. Eksp. Teor. Fiz. 91,220-234 (1986)
Random Matrix Theories in Quantum Physics: Common Concepts
Random matrix theory: Wigner-Dyson statistics and beyond.
Random-Matrix Theory of Quantum Transportr

E. H. Lieb, Phys. Rev. 162, 162 (1967)

D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)
R. Moessner, K. S. Raman, arXiv:0809.3051
Notes from the session

V. Khemani, A. Lazarides, R. Moessner, S. L. Sondhi, Phys. Rev. Lett. 116, 250401 (2016)
D. V. Else, B. Bauer, C. Nayak Phys. Rev. Lett. 117, 090402 (2016)
D. Abanin, W. De Roeck, F. Huveneers, W. W. Ho arXiv:1509:05386
D. V. Else, B. Bauer, C. Nayak arXiv:1607.05277

Castellani, Cavagna - Spin-Glass Theory for Pedestrians
Mezard, Parisi, Virasoro - Spin-Glass Theory and Beyond

E. Witten, Integrable Lattice Models From Gauge Theory, arXiv:1611.00592
Annotated version of notes
Background slides

Theory of Bound States in a Random Potential, J. Zittartz and J. S. Langer, Phys. Rev. 148, 741 (1966)

arXiv:1606.02318

D. P. Arovas and A. Auerbach, Phys. Rev. B 38, 316 (1988)
A. Auerbach, Interacting Electrons and Quantum Magnetism, Springer, 1994, Ch.16-18
A. Auerbach and D. P. Arovas, Schwinger Bosons Approaches to Quantum Antiferromagnetism, Ch. 14 in Introduction to Frustrated Magnetism

J. Maldacena, S. H. Shenker, D. Stanford, arXiv:1503.01409
Talk by D. Stanford on YouTube

Video of Kitaev's talk at KITP
Slides from Kitaev's talk

Chapter 8 of John Cardy's book "Scaling and Renormalization in Stat. Phys."
Section 4 of this review article from Thomas Vojta arXiv:1301.7746

I. Affleck, Field Theory Methods and Quantum Critical Phenomena
Phys. Rev. Lett. 59, 799 (1987)
Comm. Math. Phys. Volume 115, Number 3 (1988), 353-528
Notes from the session

Patrick Dorey, Exact S-matrices, arxiv:hep-th/9810026
Mussardo (1992), Phys. Rep. 218, 215-379
Mussardo, Giuseppe. Statistical field theory. Oxford Univ. Press, 2010.
Zamolodchikov, A.B. and Zamolodchikov, Al.B. (1979), Ann. Phys. 120, 253-291

J. Alicea and P. Fendley, ‘Topological phases with parafermions: theory and blueprints’, arXiv:1504.02476
P. Fendley, ‘Parafermionic edge zero modes in Z_n-invariant spin chains’, J. Stat. Mech. Theor. Exp. (2012), 11, P11020
A. S. Jermyn, R. S. K. Mong, J. Alicea, and P. Fendley, ‘Stability of zero modes in parafermion chains’, Phy. Rev. B (2014), 90

P.W. Kasteleyn, Physica 27 (12): 1209–1225 (1961)
H. N. V. Temperley & M. E. Fisher, Philosophical Magazine, 6:68, 1061-1063 (1961)
M. E. Fisher Phys. Rev. 124, 1664 (1961)
Les Houches notes by Richard Kenyon
Notes from the session

'The critical properties of the two-dimensional XY model', JM Kosterlitz
'Ordering, metastability and phase transitions in two-dimensional systems', JM Kosterlitz and DJ Thouless
Caltech lectures on `Topics in Statistical Mechanics and Critical Phenomena', OI Motrunich
Imperial college lectures on `The Kosterlitz-Thouless Transition', HJ Jensen
Illinois lectures on `The Berezinskii-Kosterlitz-Thouless transition', AJ Leggett
Notes from the session

Berry's original paper
The "interacting" version of the TKNN paper
The Dirac cone perspective

Keldysh - Diagram Technique for Nonequilibrium Processes
Kamenev - Introduction to the Keldysh Formalism
Rammer - Quantum Field Theory of Non-Equilibrium States

P. W. Anderson Phys. Rev. 109, 1492 (1958)
Journal of Physics C: Solid State Physics, 6, 1734 (1973)
Phys. Rev. Lett. 78, 2803 (1997)

Hofstadter paper
http://mcs.open.ac.uk/mw987/Published%20papers/paper10.pdf

A review and introductory paper by Hugo Touchette: arXiv:1106.4146 , arXiv:0804.0327
Some more mathematical notes by Richard Ellis here
An accessible review of some of the key results here
Notes from the session

Ken Wilson's original NRG for the Kondo Model (lots of interesting background, but quite expansive!): Rev. Mod. Phys. 47, 773 (1975)
A significantly clearer, detailed "instruction manual" for NRG for the Anderson Impurity Model: Phys. Rev. B 21, 1003 (1980)
Ralf Bulla's 2008 NRG review - now the standard NRG reference, with good discussion of applications: Rev. Mod. Phys. 80, 395 (2008)
NRG formulated in terms of tensor networks/ MPS: Phys. Rev. B 86, 245124 (2012)
Notes from the session

P.W. Anderson, Phys. Rev. Lett. 18, 1049 (1967)
K. D. Schotte and U. Schotte, Phys. Rev. 182, 479 (1969)
Notes from the session

Bosonization for Beginners --- Refermionization for Experts by J. von Delft, H. Schoeller
An introduction to bosonization by D. Sénéchal
Notes from the session

Chapter 9 of "The big yellow book" (Conformal Field Theory by Di Francesco et al)
2. Chapter 14 (pages 347-424) of "Polygons, Polyominoes and Polycubes" by Jesper Jacobsen, available here

A short and important background paper is the one by Thouless here, this paper only covers a specific aspect.
A more general review of theory is by Beenakker here

Loh and Carlson, PRL 97, 227205 (2006)

Review paper here
Spin liquid lecture notes here

Original paper here
Notes by Vincent Pasquier arXiv:hep-th/9405104

The main reference is the paper by Kitaev arXiv:quant-ph/9707021
Also be using some chapters from Pachos’ book, Introduction to Topological Quantum Computation. The relevant sections of the book may be found in the lecture notes here

The main reference is the lecture notes by Faddeev arXiv:hep-th/9605187

The most physical and concise introduction to weak localisation that I know of is by Khmelnitskii here
Those who would prefer something more detailed (and with better type-setting) should look at a standard review by Lee and Ramakrishnan Rev. Mod. Phys. 57, 287 (1985)
The original papers on conductance fluctuations are Altshuler and Lee & Stone

A general introduction: arXiv:1211.5623
Detailed calculations: PRB 84, 235108

This review paper up to Sec. 6.3

FDM Haldane, Fractional Statistics in Arbitrary Dimension PRL 67, 937 (1991)
Yong-Shi Wu, Statistical Distribution for Generalized Ideal Gas of Fractional Statistics Particles PRL 73. 922 (1994)
If one were careful about giving credit where it is due, I note that some of the key results of the Y-S Wu paper were published earlier here PRD 45, 4706 (1992)

Following the review paper

The original paper by Lieb and Robinson
A more recent approach taken by Hastings
Consequences of the Lieb-Robinson bounds that are given in this set of lecture notes (also by Hastings)

Roughly follow Chapters 1-3 in the lecture notes by Gerald Dunne arXiv:hep-th/9902115
References to the original literature are given at the end of these notes.

(i) Peskin, An Introduction to Quantum Field Theory, Section 19.1.
(ii) Fujikawa, PRL 42, 1195 (1979) http://prl.aps.org/pdf/PRL/v42/i18/p1195_1

TWB Kibble 1976 J. Phys. A: Math. Gen. 9 1387
WH Zurek Nature 317, 505 (1985)
Notes from the session

Mostly based on the papers below by Grover and Ch. 6 of Nielsen and Chuang.
arXiv:quant-ph/9706033 (L. K. Grover, Phys. Rev. Lett. 79, 325 (1997))
arXiv:quant-ph/9605043

Pages 1-15 of arXiv:cond-mat/9707301
The first few chapters of the book by Mehta

Peierls instability - see Chapter 2 of 'More Surprises in Theoretical Physics' by Peierls
Peierls proof of order in the Ising model - see R. B. Griffiths, Phys. Rev. 136, A437 (1964)

M. Kohmoto, L. P. Kadanoff, and C. Tang, Phys. Rev. Lett. 50, 1870 (1983)

D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)

See S. R. White, Phys. Rev. Lett. 69, 2863 (1992)

Lecture notes by Tony Leggett
Volovik and Gorkov

Exact solution for the X-ray absorption and emission of metals: Phys. Rev. 178, 1097 (1969)

J. Phys. C: Solid State Phys. 8 L49 (1975)

Phys. Rev. Lett. 49, 405 (1982)
Physics Reports
Annals of Physics Volume 160, Issue 2, 1 April 1985, Pages 343–354

Rev. Mod. Phys. 66, 129 (1994)

Rev. Mod. Phys. 51, 591 (1979)

Imry-Ma: Phys. Rev. Lett. 35, 1399 (1975)
The Harris criterion: J. Phys. C: Solid State Phys. 7 1671 (1974)
Griffiths phases: Phys. Rev. Lett. 23, 17 (1969)

Rev. Mod. Phys. 59, 1 (1987)

Phys. Rev. Lett. 43, 1434 (1979)
Phys. Rev. B 50, 3799 (1994)

Phys. Rev. Lett. 59, 799 (1987)
Comm. Math. Phys. Volume 115, Number 3 (1988), 353-528

Exact results for the Kondo problem I: Phys. Rev. B 1, 1522 (1969)
Exact results for the Kondo problem II: Phys. Rev. B 1, 4464 (1970)
A poor man's derivation of scaling laws for the Kondo problem: J. Phys. C: Solid State Phys. 3 2436 (1970)

Rev. Mod. Phys. 36, 856 (1964)

Phys. Rev. 119, 1153 (1960)
Phys. Rev. 118, 1417 (1960)

Feynman on liquid Helium: Phys. Rev. 94,262 (1954) and Phys. Rev. 138, A442 (1965)
Antiferromagnetic spin chains: Annals of Physics 16, 407-466 (1961)

Rev. Mod. Phys. 69, 731 (1997)

Phys. Rev. Lett. 50, 1153 (1983)
Nuclear Physics B, Volume 336, Issue 3, 4 June 1990, Pages 457-474
Physics Letters A,Volume 93, Issue 9, 14 February 1983, Pages 464-468