A series of perturbations

Things are a mess in OGC right now. Furniture is being replaced in all rooms, at godawful hours when I should be asleep. I've had to rifle through the underwear of an introvert, then was so disgusted I left my room in haste and locked myself out. This morning, they decided to fix a hole in my wall, at a time of their choosing. I struggled to Dbar with my sleeping bag to find a couch, only to be woken up because they decided to fix the pool table. No wonder I've been having bad dreams.

I must report to you more perturbations. While fixing a hole in my wall, they botched up the painting around the wall. The next day I was chased out of my room by painters. The day after that, I was again awoken because they decided to emboss my door with my room number. Such embossing may have benefitted you, and I wished to tell them it is no longer necessary. I endured the last of the indignities.

While requestioning what a particle is, I decided to approach quantum field theory from a different perspective. After a few years in condensed matter, I am burning with questions about field theory. Why is it so ubiquitous? Or is its ubiquity justified by a fallacy? What are there field theories where the Hamiltonian is zero? I started reading Zee's QFT in a nutshell. The writing is not stripped of mathematics, rather it presents the minimum amount of mathematics to convey the essential physical ideas through the shortest possible path. It's quite an achievement. I find I am falling in love with QFT again. The first time was over a series of lectures by Polyakov.

There are many insights here. One treasure: why do we need QFT in condensed matter? Because phonons are created when we tap on a crystal. Electrons in bands can absorb a photon and be ejected to a higher band, leaving behind a hole which acts as an independent particle. Because to describe the creation and annihilation of particles, one needs QFT. Schrodinger's equation describes the unitary evolution of a collection of particles, and as such the number of particles must remain fixed for all time.

I am flattered that I can instill urgency in you. Probably I need to distill some urgency out of my life. The hustle of day-to-day research can be overwhelming, and it is so easy to slip into a packaged role and ask simple questions to which there are simple answers. I need to expand my mind and talk to brilliant people. I don't do this enough.

I think you take 'no elementary particles' too literally. I speak of a healthy suspicion toward any particle that is claimed to be elementary. Who knows if the turtles really goes down forever, I am merely saying we should find out. I like how our expansive science is. It seems to consistently defy any egocentric world view. People may lament their loss of identity, an identity forged from a sense of special that relies on improbability. But you say, we make sense in a way that is universal. For this view, I cherish you.

Religion of emergence

When first I ate at Ajihei, I thought the experience satisfactory but not remarkable. After years of hunting and tasting and taste-developing, Ajihei’s stature has only grown, casting ever-deepening shadows on its competitors. I recommended to Zhoushen the chirashi bowl, and picked for myself the Hokkai don, which combines salmon, salmon roe, squid, scallop and sea urchin roe. The last a moist collection of brown egg sacs, pungent in taste, exquisite in pleasure. Since it is his first time, I insisted on sharing an unagi sushi, a rare indulgence. Zhoushen asked if I had a religion. The religion of emergence, I replied. More is different. More and different. Microscopic degrees of freedom organize and produce qualitatively different physics.

Lately, I have become confused by what a particle is. An object, localized when measured, sometimes massive, sometimes massless, it must interact with other particles lest we never see it anyway.

Kitaev: a particle is defined by whatever survives in the long-wavelength limit. A representation of a local operation, he says. Particles fuse together in this limit – sometimes a particle survives, sometimes no particle remains, and we return to vacuum. Fusion: an evocative, but deeply puzzling word. I am still trying to grasp its meaning. If it at all describes nature.

The elementary particles live in everyday, everywhere vacuum, and they are a collection of fermions and gauge bosons. Then there are emergent particles which pop out of existence from a condensed-matter medium, they ‘take a life of their own’ at energies much smaller than the scale set by the microscopic constituents of this medium. We cannot assume emergent particles obey the same laws that govern the microscopic medium. Very often they do not. An example is the collective excitation of a crystal – a phonon. More remarkable are the spinons and gauge bosons that appear in the low-energy theory of a quantum spin liquid.

For a long time I thought the rabbit hole only goes down. That the fundamental particles are the deep mysteries. Wen says these are the five great mysteries in nature. Why are there identical particles? Why is there Fermi statistics? Why are there gauge bosons? Why are there chiral fermions? Why is there gravity?

Why are elementary particles fundamental? In this sense the word is weakly justified: we cannot peer deeper, into vacuum’s minute folds. Elementary particles are as microscopic as can be measured. This doesn’t feel entirely satisfactory. It also hasn’t stopped anybody from guessing the turtle that lies underneath. Is our vacuum a condensed string-net, light a fluctuation of the string-net, and electrons the ends of the strings? Polyakov: turtles all the way down. It’s a heady feeling. It’s the religion of emergence. Postulate one: there are no elementary particles.

There is a growing school of thought in my mind, that diversity is every bit as amazing. In reaching for the first building blocks of nature, where she is most symmetrical (even super-symmetrical), I forget that symmetry- breaking results in particles having different masses, produces such rich diversity of building blocks that themselves organize and build the next level of maddening diversity. I forget that diversity can emerge from media without symmetry breaking – this new concept we call quantum order. Somehow, we arrive at consciousness. Postulate two: our laws must allow for consciousness.

I got my first taste of quantum spin liquids during a summer school I organized. Seventy-five students, some of whom flew across oceans for a four-day event. The Princeton name reaches far. I have never met so many strangers who would spontaneously approach me to shake my hand. I am the conduit to their happiness, and their gratitude is effusive.

I learned something about matrix product states, a highly-compressed representation of a many-body wavefunction. I asked Steve whether these representations imply a deep truth about nature. He asked me why we represent a thermal state as a superposition of a thermodynamically-large number of energy eigenstates. This isn’t an efficient representation of nature. He proposes to find a representation which superposes only a few low-entangled states.

From beside, I admire Huse’s grizzled intensity, the way he focuses and never lets go of the speaker, a hound dog who’s found its scent. His breadth of knowledge is astonishing, his insights are so quickly realized and deeply cutting, only veteran speakers are unfazed.

I reserved forty-six tables for a dinner in the Sky room of Triumph – I had to guarantee a minimum expenditure of 750 with my own card. It looked like a failed venture when thirty students showed up. I encouraged merry-making, recommended the beer sampler and had two myself. I joined a table of Taiwanese stragglers whose late appearance bolstered the bill, and discussed physics late into the night.