Xueda Wen | Floquet conformal field theory and beyond

Xueda Wen | Floquet conformal field theory and beyond

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00:00
all right so let's begin shadow in my teeth so this is the reason it works with separator did help with a photo
00:26
Mikey and everybody audience and you made a poster at our and I also introduced some works in progress okay so first let me start from a vision so we have seen a lot of our studied law at this rate then we we have similarly curious if any any people have stabbed you love most Peter Bowman field theory
01:03
research literature in the fan any any mobile or can all theory so so I remove whatever even the very simple people what study we are simply curious the author okay this is our motivation and there are also some mathematical motivation this is called a complex so
01:40
now if we start complex plane we start from some point then we there are mapping ha map this point to the other point we do this making on and on for many times then we have and although these products either flow through infinity or this one will move little bit locally inside the some
02:12
region I believe most of us have seen this kind of plot so in this part if we start from some point even dark in the start region we add this other function or many times the corner here we have flow to infinity it is like original when her so how many times do you add function on this plot it was simply to
02:47
say that this pattern function if you send another another very beautiful but there are only two regions the light they have a very different behaviors so we we often put in curious is this hello pure pure pure mathematics any non equilibrium dynamics
03:19
in physics okay our mathematical equation okay so the structure of these talking at a Bollywood first I introduced a 140 then I will give some simple generalization to run random range or even say a tea cosy periodically driven [Music] okay let me first
03:59
Oh mentioned simply means that you drive the system periodically in okay so what do I mean by trying with the system in time here I think we mean we consider a time point here T capital T the standard Heather are you see ft 0 0 is nothing but the Hamiltonian density we simply
04:29
put I'm a little function at time dependent function okay the the physical meaning is very simple we simply deformed Hamiltonian dedicated at the function of time and see what happened for this reaction okay so for the flow panic killed simply mean the dysfunctional have periodic period time T similarly you can either call it periodically or randomly using fully
05:03
modified it's how this function depend on time okay very simple okay so in one last month museum Kia the warrior component of this component is a composed of a virus or a generator I wish since why the the well-known alerts are Edgar okay what I want to save that challenging to solve this problem for arbitrary app is very average not easy
05:36
to solve but now start from some simple choice we start from some simple choice of app once we can understand some simple case then so the simple choice of its app we have a speed have because I mean compiled over L
06:07
as here actually the space so why I took this form because if you choose this kind of app you can fun the Fourier component of the hoodie it's composed of only three generators L 0 L N and L minus n that's right there and you thought about it apart well this 3 generator that form a closed algebra which is a way to go caliber and easier to handle
06:40
it's problem solvers because it's problem solved in the time-independent case independent of you yeah it's like ok you have in the general idea our argument is going to to drive the
07:13
CFG with the virus or an algebra which is evening there's no but now in the initial effort we will drive the cfq in the as a little algebra which is simpler and we will see there are already nancylou features in the union is a very simple kind of driving there's some new feature vision what do you mean by kitchen oh sorry
07:46
yeah yeah so start from a very concrete example okay we need to our time independent we call it zero and it's one so it's zero in nothing but a 20-week uniform with the uniform have included st uniform use bits we have open border and it's one
08:19
very simple equation which i jus that sine square PI x over L this is Islam works simple choice I will tell you okay we will fix with the 2020s 0 and H 1 we drive the system a with this one for time period t 1 we switch to a serial port I'm Kitty row we repeat this
08:49
procedure on data some other initial State ok then let me tell you the result first because now I is 0 and H 1 well the only parameter that I can cure a Camaro and Qi at the time period so this diagram this diagram and the functional
09:22
TV rule and she what right so any possible scale is there a relative energy scale and Kyra to lose any freedom when you fix it like this because I could imagine that there is a relative energy scale because mr. H
09:54
0 and H 1 okay yeah okay so it's really possible nothing interesting happen parameter space but first this is zero or we found
10:45
there are two you mean what do you mean by a given the face okay distinguish two different face we simply spot either in a system we found that unison graduated in his reason but you can imagine a grows linearly in time all the way in this blue region the battery simply oscillates ultimate all the way all the
11:17
way it's never curled up so we're going to give the name of heating phase although this is not good name because conditioning the in conformity with growth luggage okay so good you know diagram giving husk so I don't
11:55
mean I said the Omega is the same Omega is the frequency theorem oh good oh my gosh is not mean I've given it from the [Music] Omega actually depends on different points different point Omega is not the same diagram you mean okay people I introduced reminisce if we change this
12:37
to some other choice I'm sure do you like you can't carry a different of this diagram okay the club let me show you the different a phase diagram if that would be the only have two phase what is it underlying this is diagram we have a body we have this is diverse okay to say that it'll be technique but what I want is to see if the calculation of entropy essentially we are decorating
13:17
the correlated correlation function career to function we try with the system we can we can track how the operator you have so the primary operator UART when we try the system comunitaria confirmation we acted on the operator and we observe how this operator move even in the complex plane oh we have fun of it as il-2 joining
13:47
this is operator we move on a circle or a circle with the function we call it out yet on the the pod period we move along a circle its transformation very simple why does it move rather than
14:21
spreading already choose a very special each one yeah yeah actually I think is wise to them but the premier term okay
15:10
nothing to do with this integral now in a group oh so yeah the spread of the operator is rated you oxt yeah yeah OST is always very complicated operator if you think in terms of the shown in the picture it's always a very complicated oh yeah but just hide it at a complication in the location yeah yeah in the space-time right we know the
15:40
locations we are sure holidays or how the location change they made a movie with transformation so for each models chatter major have a 2x2 2x2 matrix which it as ever to see matrix so now this problem it reduced it
16:11
very simply multiply different articles in magics one by one then you can check all the operator move on the circle okay here there are three panel Mobius transformation which is which are called elliptic parabolic and hyperbolic kind of information so the correspond to the nakajima piece picking these entities can be a theory some
16:46
popular the intuitive x-ray if we have too many machines and they take the transformation now as a function of time we say how the operator move on the complex plane for the elliptic transformation this operator be somebody ultimate ultimate in time on a circle hyperbolic transformation the operator reflow will
17:20
produce um it's point information we also call by a power law behavior oh oh you're using the you're using this this de facto
19:23
but this one it spawns and if we never come back who is it is a precision okay feature if we even a few fish and we try with the system energy we must
20:28
grow which means the system doesn't absorb energy but in the keikyu phase and we try with the system the system of sub energy it's naturally in time well that was was amazing the system does not absorb energy a uniform way there are two peaks in real space in the real space actual piece which grows naturally in time and you know another
20:59
pillar this one at least are exactly the same the real space X this is time T the color on Oh indeed and you try out the system there are two energy chips formerly system this one in the numerical simulation based on xx this vision we indeed we observe this
21:33
formation of energies these are two peaks because you're driving to the side yeah driving this each of the scientists yeah you can't enjoy a pair of your function f if you change provision Oh the provision of the to keep depend on Keros you are entering a period if you face with the hammock pony trying to change Allah although change so the
22:08
always to enemy peace even if I'm driving with some analytic function no just sign I'll here is very function just everywhere okay it not easy to any
22:40
repeats but there are more amazing things with two peaks first you can follow the one keeping the Cairo the other is aunty Carol but I mean if you stop driving the system move in the other direction similarly another interesting feeling than all the entitlements sorry if you to the crappy
23:10
they just stay in the same place yeah they just stay in the same place they don't change which time at all yeah what would happen invited only observe do you know the behavior sure yeah after each cycle you would switch okay another interesting feature is that all the implements between the two kids I mean just now that that's our system you
23:57
can mentally grow their linearly in time we are all contributed by the two peaks and we drive the system each cycle we are talking the if you have hair to the tips so this is a mile I imagine the thesis there should be some also like structure okay also the driving will amplify everything what do I mean the initial stage in
24:29
children have the ground state if you through some operator in the in the initial stage if driving with my attractive political thriller spin operator with the spin it's inspiring each other you could have you enjoy the system under the two hundred Peaks I'm not another that why I arrived at over which are proportional to the the component mnh-mnh bar also there we also
25:02
found some amazing religion but little energy or the system made a proportional to the central charge time it's Fernando in ten dimensions so because you know in America through the linear rate so the totally I mean how universal our speech our bodies and so long because killing our we already started going driving our final going to study Torah
25:35
as well sorry is there me a simple reason for that image and and choke irritation no context our mana general vampires are and so we have heart of truth so the fixed point if there are
26:11
fix pond the system we always know it seemed I don't have time only two minutes to it quickly close it clear out the dragging simply let me tell every dollar first care only the drive-in there are two fifties well the closing parity the driver there
26:49
are also two fifty this diagram but for the purity is very interesting structure in random driving through this I did not get it approved almost the same as one D understand my vision you know human being although in the random Germany they're the only teaching piece this one but for
27:23
the causing all these three kisses the city of its only depend on de only depend on the the ignore exponent of the product matrix okay we could feature in a poly column pair of the body we still have three to face teaching phase and in that meeting feel about it there are some client structure evening
27:58
contra baby parrots on because they're all trying some irregular start straightening hang my entropy and what do you mean by Cauchy pure dick oh good we drive the system we carry the key it's very cute so this diagram is like a
28:46
fearsome threat to life Star Trek movies diagram some compassion or the wrath of the driver try to even see of Q we have give them the kind of a random driving but no matter how powerful but it kind of random twice into the system is always a system of you always be only in particular the you have momentum it will
29:18
always grow linearly in time for the random driving we come true we have true this theory mathematics called fürstenberg cast in Syria well what I want to mention period and all these book is talking about the product I'll be random as they are then you see magnetics there are many books I
29:52
thought many of them can be applied but this like the most important one is from the cerium I can't gather there's only one place in space and you mentally will always grow linearly time the total energy will always grow the expiry okay that's the end so the open mention we
30:28
have we want to work out some generalizations I'm gonna drive because function f which is really not a jerk but what kind of join the system can be
30:58
cruelly down we also want to understand a lot of review of sehe this tell how works both works for arbitrary yet there should be some solid work with you and it's also interesting to study the higher how how many pose to compare all of this to the say XE modem because you're saying that Energy's being a C is usually just a low-energy oh good
32:50
numerical simulations we cannot drive a very very long time very short yeah yeah can go to the slide where you wrote h h0 and which one is a very beginning yeah you just is it possible to look with each one so there's this formula for each one right can I just say that
33:22
this sign is a square root of G and say that it's the same cftc but what I am actually doing is I'm just changing metric and time yeah yeah yeah India that I can send you know the message that is visual basicnet time direction most important why can't you do it for any function why is it important to design it is it was the most well we can generalize we are
33:53
arbitrary arbitrary I'm get super CFCs you answer the field universe you but if what we come is with the peak is determined by the condition of the fixed point yeah we're in the exponent is
34:31
exponent determined by engineer

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